When light of a certain frequency is incident on a metal surface, no photoelectrons are emitted. If the frequency of the light is increased, what happens to the stopping potential?

D. The stopping potential increases.

A. The stopping potential does not change.

B. The stopping potential decreases.

C. The stopping potential can either increase or decrease, depending on the intensity of the light.

D. The stopping potential increases.

A generator manufacturing company accidentally made an AC generator instead of a DC generator. To fix this error,

D. the slip rings should be replaced with split rings

A. the magnetic field needs to be made stronger

B. the split rings should be replaced with slip rings

C. the number of turns of the armature coil needs to be decreased

D. the slip rings should be replaced with split rings

The pinhole camera works on

B. the principle of the rectilinear propagation of light

A. the principle of the reversibility of light

B. the principle of the rectilinear propagation of light

D. the principle of total internal reflection of light

Which of the following is an example of a couple?

B. The forces that are applied to the handle of a screwdriver when you twist it.

C. The forces that are applied to a cross wench to loosen or tighten the lug nuts on a wheel of a car.

D. The forces that are applied to the steering wheel of a car when you turn it.

When a water droplet is placed on a freshly cut piece of wood, it spreads out to form a thin layer because the wood is

A. not at equilibrium with the water

C. at equilibrium with the water

In an AC circuit, resonance occurs when the impedance of the circuit is:

C. Equal to the capacitive reactance of the circuit

Which of the following thermometers measures temperature from the thermal radiation emitted by objects?

B. Platinum resistance thermometer

D. Constant pressure gas thermometer

A metal sphere is placed on an insulating stand. A negatively charged rod is brought close to it. If the sphere is earthed and the rod is taken away, what will be the charge on the sphere?

C. The sphere will have a net positive charge.

A. The sphere will remain neutral.

B. The sphere will have a net negative charge.

C. The sphere will have a net positive charge.

D. The sphere will become polarized

An object is placed 35 cm away from a convex mirror with a focal length of magnitude 15 cm. What is the location of the image?

C. 26.25 cm in front of the mirror

D. 10.5 cm in front of the mirror

The pitch of a musical note is determined by the frequency of the sound wave that it produces. If two instruments have the same frequency, which of the following factors will most affect the difference in their pitches?

D. The material of the instrument

The number of holes in an intrinsic semiconductor

C. is equal to the number of free electrons

A. is not equal to the number of free electrons

B. is greater than the number of free electrons

C. is equal to the number of free electrons

D. is less than the number of free electrons

A positively charged particle is placed near a negatively charged particle. What is the direction of the electric force between the two particles?

D. The electric force is directed from the positive particle to the negative particle.

A. The electric force is directed from the negative particle to the positive particle.

C. The direction of the electric force cannot be determined.

D. The electric force is directed from the positive particle to the negative particle.

Which of the following statements is correct about the angle of dip at various points on Earth?

A. The angle of dip is zero at the equator and 90 degrees at the magnetic poles.

B. The angle of dip is greater at higher altitudes than at lower altitudes

C. The angle of dip is positive in the northern hemisphere and negative in the southern hemisphere.

D. The angle of dip is constant at all points on Earth

JAMB 2023

2023 JAMB Physics Past Questions and Answers

The 2023 JAMB Physics past questions with answers: 65 objective questions from the 2023 paper in the DeeepSolve question bank, each with its answer behind "Show answer". Try each question before you check, then practise the paper as a timed JAMB-style CBT.

Practise this paper as a timed JAMB-style CBT All JAMB Physics years

Questions

1.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
2.
Rainbow formation is as a result of the combination of which of the following phenomena? (i) Reflection (ii) Dispersion (iii) Total internal reflection (iv) Refraction
1. A.(ii) and (iv) only
2. B.(i), (iii) and (iv) only
3. C.(ii), (iii) and (iv) only
4. D.(i), (ii) and (iv) only
Show answer
Answer: C. (ii), (iii) and (iv) only
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3.
Which of the following materials is a good insulator?
1. A.Silver
2. B.Water
3. C.Rubber
4. D.Copper
Show answer
Answer: C. Rubber
AI explanation
1. Analyze the question
The question asks you to identify which of the listed materials is a "good insulator." In physics, an insulator is a material that resists the flow of electric current because its electrons are tightly bound to their atoms and are not free to move.
2. Explain the concept
Conductors: These are materials that allow electric current to flow through them easily. They have "free electrons" that move freely throughout the material. Metals like silver, copper, and aluminum are excellent conductors.
Insulators: These are materials that do not allow electric current to flow through them. They have very few or no free electrons. Examples include rubber, glass, plastic, and dry wood.
Water: Pure water is a poor conductor, but the water we encounter in daily life (tap water, rain water) contains dissolved minerals and salts, which makes it a conductor.
3. Show the solution
Option A (Silver): Silver is a metal and is actually the best conductor of electricity among all metals. Therefore, it is not an insulator.
Option B (Water): As mentioned, water (especially tap water) contains ions that allow electricity to pass through it. It is considered a conductor in most practical scenarios.
Option C (Rubber): Rubber has a very high electrical resistance. It does not allow electrons to flow through it, which is why it is used to coat electrical wires to prevent shocks. It is a classic example of an insulator.
Option D (Copper): Copper is the most common material used for electrical wiring in our homes because it is a very good conductor of electricity.
4. Identify the answer
Comparing the options, Rubber is the only material listed that prevents the flow of electricity.
5. Exam Tip
When you see questions about conductors and insulators, remember the "Free Electron Rule": If the material has free electrons, it is a conductor (metals). If it holds its electrons tightly, it is an insulator (non-metals like rubber, plastic, or glass).
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4.
Which of the following liquids has the highest surface tension?
1. A.Soapy water
2. B.Water
3. C.Mercury
4. D.Oil
Show answer
Answer: C. Mercury
AI explanation
Analysis
The question asks us to identify which of the listed liquids possesses the highest surface tension. Surface tension is the property of a liquid surface that allows it to resist an external force, caused by the cohesive forces between liquid molecules.
Concept Explanation
Surface tension depends on the strength of the cohesive forces between the molecules of the liquid.
Water has relatively high surface tension due to strong hydrogen bonding.
Soapy water has a lower surface tension than pure water because soap acts as a surfactant, breaking the hydrogen bonds and reducing the cohesive forces.
Oil generally has lower surface tension than water because its intermolecular forces are weaker (van der Waals forces).
Mercury is a liquid metal. It has extremely strong metallic bonds between its atoms, which results in very high cohesive forces. This is why mercury forms spherical beads rather than spreading out on surfaces.
Step-by-Step Solution
Compare the nature of the liquids: We are comparing a polar liquid (water), a surfactant-treated liquid (soapy water), a non-polar liquid (oil), and a metallic liquid (mercury).
Evaluate cohesive forces: • Soapy water is designed to lower surface tension to help with cleaning. • Water has high surface tension, but it is significantly lower than that of liquid metals. • Mercury's metallic bonding is significantly stronger than the hydrogen bonding found in water or the weak forces in oil.
Conclusion: Because mercury has the strongest intermolecular (metallic) forces among the options provided, it exhibits the highest surface tension.
Identify the Answer
Comparing the options, Mercury (C) is well-known in physics for having a surface tension value (approx. 0.48 N/m) that is much higher than that of water (approx. 0.072 N/m).
Exam Tip
When you see questions about surface tension, remember: "The stronger the attraction between the molecules, the higher the surface tension." Metals in liquid form (like mercury) will almost always have higher surface tension than common organic liquids or water.
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5.
A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young's modulus for the material of the wire. [Take g = 10 ms $^{-2}$ ]
1. A. $2.4×10^{10}(Nm^{-2})$
2. B. $1.5×10^{10}(Nm^{-2})$
3. C. $2.4×10^9(Nm^{-2})$
4. D. $1.3×10^{10}(Nm^{-2})$
Show answer
Answer: A. $2.4×10^{10}(Nm^{-2})$
AI explanation
Analysis
To solve this problem, we need to calculate the Young's Modulus ( $Y$ ) of the wire material. Young's Modulus is defined as the ratio of tensile stress to tensile strain.
Concept
The formula for Young's Modulus is:
$Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L}$
Where:
$F$ = Force (Weight = $mg$ )
$A$ = Cross-sectional area of the wire ( $\pi r^2$ )
$\Delta L/L$ = Tensile strain (given as a percentage)
Step-by-Step Solution
1. Identify the given values:
Radius ( $r$ ) = $0.2 \text{ mm} = 0.2 \times 10^{-3} \text{ m} = 2 \times 10^{-4} \text{ m}$
Load ( $m$ ) = $1.5 \text{ kg}$
$g = 10 \text{ ms}^{-2}$
Strain ( $\frac{\Delta L}{L}$ ) = $0.5\% = \frac{0.5}{100} = 0.005 = 5 \times 10^{-3}$
2. Calculate Force ( $F$ ):
$F = mg = 1.5 \times 10 = 15 \text{ N}$
3. Calculate Cross-sectional Area ( $A$ ): Using $\pi \approx 3.142$ :
$A = \pi r^2 = 3.142 \times (2 \times 10^{-4})^2$
$A = 3.142 \times 4 \times 10^{-8} \approx 1.2568 \times 10^{-7} \text{ m}^2$
4. Calculate Young's Modulus ( $Y$ ):
$Y = \frac{F}{A \times (\Delta L/L)}$
$Y = \frac{15}{(1.2568 \times 10^{-7}) \times (5 \times 10^{-3})}$
$Y = \frac{15}{6.284 \times 10^{-10}}$
$Y \approx 2.387 \times 10^{10} \text{ Nm}^{-2}$
Rounding this value to two significant figures gives approximately $2.4 \times 10^{10} \text{ Nm}^{-2}$ .
Conclusion
Comparing our result to the given options, it matches option A.
Exam Tip
When dealing with units in elasticity questions, always convert millimeters (mm) to meters (m) immediately. A common mistake is forgetting to square the radius or forgetting to convert the percentage strain into a decimal. Keep your powers of 10 organized to avoid calculation errors!
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6.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
7.
A man swung an object of mass 2 kg in a circular path with a rope 1.2 m long. If the object was swung at 120 rev/min, find the tension in the rope.
1. A.400
2. B.288
3. C.240
4. D.379
Show answer
Answer: D. 379
AI explanation
1. Analyze the question
We are given:
Mass ( $m$ ) = 2 kg
Radius ( $r$ ) = 1.2 m
Frequency ( $f$ ) = 120 revolutions per minute (rev/min)
We need to find the tension ( $T$ ) in the rope, which acts as the centripetal force ( $F_c$ ).
2. Explain the concept
The tension in a rope swinging an object in a horizontal circle is equal to the centripetal force. The formula for centripetal force is:
$F_c = m \omega^2 r$
Where:
$m$ is the mass
$\omega$ (omega) is the angular velocity in radians per second (rad/s)
$r$ is the radius
First, we must convert the frequency from rev/min to rev/s:
$f = \frac{120 \text{ rev}}{60 \text{ s}} = 2 \text{ rev/s (or Hz)}$
Next, convert frequency to angular velocity ( $\omega$ ) using the formula $\omega = 2\pi f$ :
$\omega = 2 \times \pi \times 2 = 4\pi \text{ rad/s}$
3. Show the solution
Now, substitute the values into the centripetal force formula:
$T = m \times \omega^2 \times r$
$T = 2 \times (4\pi)^2 \times 1.2$
$T = 2 \times (16\pi^2) \times 1.2$
$T = 2 \times 16 \times 9.87 \times 1.2$ $(using$ \pi^2 \approx 9.87 $)$
$T = 315.84 \times 1.2$
$T \approx 379.008 \text{ N}$
Rounding to the nearest whole number, we get 379 N.
4. Identify the answer
Comparing our result with the options provided, the correct option is D.
5. Tip
When dealing with circular motion problems in JAMB, always ensure your angular velocity ( $\omega$ ) is in radians per second. If the question gives you revolutions per minute, divide by 60 first to get Hertz, then multiply by $2\pi$ . Also, remember that $\pi^2$ is approximately 9.87, which is often useful for quick calculations!
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8.
When light of a certain frequency is incident on a metal surface, no photoelectrons are emitted. If the frequency of the light is increased, what happens to the stopping potential?
1. A.The stopping potential does not change.
2. B.The stopping potential decreases.
3. C.The stopping potential can either increase or decrease, depending on the intensity of the light.
4. D.The stopping potential increases.
Show answer
Answer: D. The stopping potential increases.
AI explanation
1. Analyze the Question
The question asks about the relationship between the frequency of incident light and the stopping potential in the photoelectric effect. Specifically, it asks what happens to the stopping potential when the frequency of the incident light is increased.
2. Explain the Concept
The photoelectric effect is governed by Einstein’s photoelectric equation:
$hf = \Phi + K_{max}$
Where:
$h$ is Planck’s constant.
$f$ is the frequency of the incident light.
$\Phi$ (Work function) is the minimum energy required to remove an electron from the metal surface.
$K_{max}$ is the maximum kinetic energy of the emitted photoelectrons.
The stopping potential ( $V_s$ ) is the negative potential applied to the anode to stop the most energetic photoelectrons. It is directly related to the maximum kinetic energy by the equation:
$K_{max} = eV_s$
(where $e$ is the charge of an electron).
Combining these, we get:
$eV_s = hf - \Phi$
$V_s = \frac{hf}{e} - \frac{\Phi}{e}$
From this equation, you can see that the stopping potential ( $V_s$ ) is directly proportional to the frequency ( $f$ ) of the incident light. As the frequency increases, the energy of the photons increases, which gives the emitted electrons more kinetic energy, requiring a higher (more negative) potential to stop them.
3. Show the Solution
Step 1: Identify the relationship: $V_s = \frac{hf - \Phi}{e}$ .
Step 2: Observe the effect of increasing $f$ : Since $h$ , $e$ , and $\Phi$ are constants for a given metal, increasing $f$ makes the term $(hf - \Phi)$ larger.
Step 3: Conclude the result: Because $(hf - \Phi)$ increases, $V_s$ must also increase to effectively stop the faster-moving electrons.
4. Identify the Answer
The correct option is D. The stopping potential increases as the frequency of the incident light increases.
5. Exam Tip
Always remember the "Frequency-Energy Connection": In the photoelectric effect, frequency determines the energy (and thus the stopping potential) of the electrons, while intensity determines the number of electrons emitted. If you see "frequency" in a question, think "energy/potential."
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9.
Which of the following is a type of incandescent light source?
1. A.Fluorescent lamp
2. B.LED lamp
3. C.Tungsten filament lamp
4. D.Neon lamp
Show answer
Answer: C. Tungsten filament lamp
AI explanation
Analysis
The question asks us to identify an "incandescent" light source from the given options. To answer this, we must understand what the term "incandescence" means in physics.
Concept Explanation
Incandescence is the emission of light caused by heat. In an incandescent light source, an electric current passes through a filament (usually made of a material with a high melting point), causing it to become so hot that it glows and emits visible light.
Fluorescent lamps (Option A): These work through gas discharge and fluorescence, not heat. They use ultraviolet light to excite a phosphor coating.
LED lamps (Option B): These use electroluminescence, where light is produced by the movement of electrons in a semiconductor material.
Tungsten filament lamps (Option C): These contain a thin wire (filament) made of tungsten. When electricity flows through it, the resistance causes the wire to heat up to a very high temperature, resulting in the emission of light. This is the classic definition of an incandescent source.
Neon lamps (Option D): These are gas-discharge lamps that produce light by ionizing neon gas with high voltage.
Step-by-Step Solution
Define Incandescence: Incandescence is light produced by thermal radiation (heat).
Evaluate the options: • A, B, and D rely on gas discharge or semiconductor physics (luminescence). • C relies on the heating of a metal filament (thermal radiation).
Conclusion: Since the tungsten filament lamp produces light specifically because the filament is heated to incandescence, it is the correct answer.
Exam Tip
When you see the word "incandescent," think "Heat = Light." If the light source gets very hot to the touch while operating (like the old-fashioned bulbs), it is almost certainly an incandescent source.
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10.
A 35 kΩ is connected in series with a resistance of 40 kΩ. What resistance R must be connected in parallel with the combination so that the equivalent resistance is equal to 25 kΩ?
1. A.40 kΩ
2. B.37.5 kΩ
3. C.45.5 kΩ
4. D.30 kΩ
Show answer
Answer: B. 37.5 kΩ
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11.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
12.
A charge of $4.6 × 10^{-5}$ C is placed in an electric field of intensity $3.2 × 10^4$ $Vm^{-1}$ . What is the force acting on the electron?
1. A.1.5 N
2. B.3.7 N
3. C.4.2 N
4. D.2.5 N
Show answer
Answer: A. 1.5 N
AI explanation
Analysis
To solve this problem, we need to understand the relationship between an electric field, the charge placed within it, and the resulting force exerted on that charge.
Concept
The electric field intensity ( $E$ ) is defined as the force ( $F$ ) per unit charge ( $q$ ) acting on a charge placed in an electric field. The formula is:
$E = \frac{F}{q}$
To find the force ( $F$ ), we rearrange the formula:
$F = q \times E$
Where:
$F$ = Force (measured in Newtons, N)
$q$ = Charge (measured in Coulombs, C)
$E$ = Electric field intensity (measured in Volts per meter, $Vm^{-1}$ or Newtons per Coulomb, $NC^{-1}$ )
Step-by-Step Solution
Identify the given values: • Charge ( $q$ ) = $4.6 \times 10^{-5} \, \text{C}$ • Electric field intensity ( $E$ ) = $3.2 \times 10^4 \, \text{Vm}^{-1}$
Apply the formula: $ $F = (4.6 \times 10^{-5}) \times (3.2 \times 10^4)$ $
Perform the calculation: • Multiply the coefficients: $4.6 \times 3.2 = 14.72$ • Multiply the powers of 10: $10^{-5} \times 10^4 = 10^{-1}$ • Combine them: $14.72 \times 10^{-1} = 1.472 \, \text{N}$
Rounding: Rounding $1.472 \, \text{N}$ to one decimal place gives us approximately 1.5 N.
Conclusion
Comparing our result to the given options, the value matches option A.
Exam Tip: When dealing with scientific notation in JAMB Physics, always multiply the numbers first, then handle the powers of 10 separately. This prevents errors with decimal placement. Also, remember that $1.472$ is very close to $1.5$ , so don't be discouraged if your exact calculation isn't listed; look for the closest approximation!
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13.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
14.
The working of the beam balance is based on the principle of
1. A.moments
2. B.conservation of energy
3. C.equivalence
4. D.floatation
Show answer
Answer: A. moments
AI explanation
1. Analyze the question
The question asks for the underlying physical principle that allows a beam balance to function. A beam balance is a device used to determine the mass of an object by comparing it with a known mass.
2. Explain the concept
The beam balance consists of a horizontal beam pivoted at its center (the fulcrum). When you place an object on one side and a known mass on the other, the system is in equilibrium.
The Principle of Moments states that for a body to be in rotational equilibrium, the sum of the clockwise moments about a pivot must equal the sum of the anticlockwise moments about the same pivot.
Moment = Force × Perpendicular distance from the pivot.
In a beam balance, the force is the weight ( $W = mg$ ). Since the distances from the fulcrum to the pans are equal, the beam balances only when the weights (and thus the masses) on both sides are equal.
3. Show the solution
Step 1: Identify the components of the beam balance: a pivot (fulcrum) and two arms of equal length.
Step 2: Recognize that the balance works by balancing the turning effect of forces on either side of the pivot.
Step 3: Recall that the turning effect of a force is called a moment.
Step 4: Since the beam remains horizontal (in equilibrium) when the masses are equal, it confirms that the clockwise moment equals the anticlockwise moment. Therefore, the device operates based on the principle of moments.
4. Identify the answer
Option A (Moments): Correct. The beam balance relies on the equality of moments to function.
Option B (Conservation of energy): Incorrect. While energy is conserved in physical systems, it is not the principle of operation for a balance.
Option C (Equivalence): Incorrect. This is not a standard principle governing simple mechanical balances.
Option D (Floatation): Incorrect. This relates to Archimedes' principle and buoyancy in fluids, which does not apply to a beam balance.
5. Exam Tip
Whenever you see questions about levers, seesaws, or beam balances, immediately think of the Principle of Moments. Remember the formula: Clockwise Moment = Anticlockwise Moment. If the distances are equal, the masses must be equal!
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15.
A step-down transformer is used on a 2.2 kV line to deliver 110 V. How many turns are on the primary windings if the secondary has 25 turns?
1. A.20
2. B.250
3. C.200
4. D.500
Show answer
Answer: D. 500
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16.
Calculate the absolute pressure at the bottom of a lake at a depth of 32.8 m. Assume the density of the water is 1 x 10^3 kgm-3 and the air above is at a pressure of 101.3 kPa. [Take g = 9.8 $ms^{-2}$ ]
1. A.422.7
2. B.220.14
3. C.464.53
4. D.321.74
Show answer
Answer: A. 422.7
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17.
A missile is launched with a speed of 75 $ms^{-1}$ at an angle of 22° above the surface of a warship. Find the horizontal range achieved by the missile. Ignore the effects of air resistance. [Take g = 10 $ms^{-2}$ ]
1. A.195
2. B.271 m
3. C.391 m
4. D.136 m
Show answer
Answer: C. 391 m
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18.
A piano wire 50 cm long has a total mass of 10 g and its stretched with a tension of 800 N. Find the frequency of the wire when it sounds its third overtone note.
1. A.800 Hz
2. B.600 Hz
3. C.400 Hz
4. D.200 Hz
Show answer
Answer: A. 800 Hz
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19.
A simple pendulum, has a period of 5.77 seconds. When the pendulum is shortened by 3 m, the period is 4.60 seconds. Calculate the new length of the pendulum
1. A.5.23 m
2. B.6.42 m
3. C.4.87 m
4. D.7.26 m
Show answer
Answer: A. 5.23 m
AI explanation
1. Analyze the Question
We are given two different periods for a simple pendulum at two different lengths. We need to find the new length ( $L_2$ ) after the original length ( $L_1$ ) was shortened by 3 meters.
2. Explain the Concept
The period ( $T$ ) of a simple pendulum is given by the formula:
$T = 2\pi\sqrt{\frac{L}{g}}$
Where:
$T$ = Period in seconds
$L$ = Length of the pendulum in meters
$g$ = Acceleration due to gravity ( $\approx 9.81 \, \text{m/s}^2$ )
Since $2\pi$ and $\sqrt{g}$ are constants, we can establish a ratio:
$\frac{T_1}{T_2} = \sqrt{\frac{L_1}{L_2}}$
Squaring both sides gives:
$\left(\frac{T_1}{T_2}\right)^2 = \frac{L_1}{L_2}$
3. Show the Solution
Step 1: Set up the equations. Let $L_1$ be the original length. The new length $L_2 = L_1 - 3$ . Given: $T_1 = 5.77 \, \text{s}$ and $T_2 = 4.60 \, \text{s}$ .
Step 2: Substitute the values into the ratio formula.
$\left(\frac{5.77}{4.60}\right)^2 = \frac{L_1}{L_1 - 3}$
$(1.2543)^2 = \frac{L_1}{L_1 - 3}$
$1.5733 = \frac{L_1}{L_1 - 3}$
Step 3: Solve for $L_1$ .
$1.5733(L_1 - 3) = L_1$
$1.5733L_1 - 4.72 = L_1$
$1.5733L_1 - L_1 = 4.72$
$0.5733L_1 = 4.72$
$L_1 = \frac{4.72}{0.5733} \approx 8.23 \, \text{m}$
Step 4: Calculate the new length ( $L_2$ ).
$L_2 = L_1 - 3$
$L_2 = 8.23 - 3 = 5.23 \, \text{m}$
4. Identify the Answer
Comparing our result to the given options, the calculated new length is 5.23 m. This matches option A.
5. Exam Tip
When dealing with pendulum period problems, always remember that the period is proportional to the square root of the length ( $T \propto \sqrt{L}$ ). If you ever forget the full formula, just remember that if you increase the length, the period increases, and if you decrease the length, the period decreases. This helps you check if your final answer makes logical sense!
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20.
Which of the following is NOT a limitation of experimental measurements?
1. A.Systematic error
2. B.Instrument resolution
3. C.Random errors
4. D.Human error
Show answer
Answer: D. Human error
AI explanation
Analysis of the Question
The question asks us to identify which of the listed factors is NOT considered a fundamental limitation of experimental measurements in the context of physics. To answer this, we must distinguish between inherent limitations of the measurement process and errors that arise from the experimenter.
Concept Explanation
In physics, experimental measurements are subject to uncertainties that prevent us from obtaining the "true" value of a physical quantity. These are categorized as follows:
Systematic Error (Option A): These are consistent, repeatable errors associated with faulty equipment or a flawed experimental design (e.g., a zero-error on a vernier caliper). They are a limitation because they shift all measurements away from the true value.
Instrument Resolution (Option B): This is the smallest change a measuring instrument can detect. It is an inherent limitation of the device itself; no matter how careful you are, you cannot measure more precisely than the smallest division on your scale.
Random Errors (Option C): These are unpredictable fluctuations in readings caused by environmental factors (like temperature changes or vibrations). They are a fundamental limitation because they cannot be completely eliminated, only minimized by taking multiple readings and finding the average.
Human Error (Option D): This refers to mistakes made by the person performing the experiment, such as misreading a scale, parallax error, or poor technique. Unlike the other three, human error is not an inherent limitation of the measurement process itself; it is a result of carelessness or lack of skill. With proper training and attention, human error can be completely avoided.
Step-by-Step Solution
Step 1: Evaluate the nature of Systematic errors, Instrument resolution, and Random errors. All three are considered "limitations" because they are bound to the physics of the measurement process or the equipment used.
Step 2: Evaluate "Human error." Because human error is caused by the experimenter's mistakes rather than the equipment or the nature of the measurement, it is classified as a "blunder" or a mistake rather than a fundamental limitation of the experimental method.
Conclusion
While systematic errors, instrument resolution, and random errors are inherent challenges in physics experiments, human error is a mistake that can be avoided with proper care. Therefore, it is not considered a fundamental limitation of the measurement process.
Exam Tip: When you see questions about "limitations" or "errors," remember: if it’s about the tool or the environment, it’s an inherent limitation. If it’s about the person holding the tool, it’s a mistake (human error).
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21.
The terminals of a battery of emf 24.0 V and internal resistance of 1.0 Ω is connected to an external resistor 5.0 Ω. Find the terminal p.d.
1. A.18.0V
2. B.12.0V
3. C.16.0V
4. D.20.0V
Show answer
Answer: D. 20.0V
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22.
An explosion occurs at an altitude of 312 m above the ground. If the air temperature is -10.00°C, how long does it take the sound to reach the ground? [velocity of sound at $0^oC$ = 331 $ms^{-1}$ ]
1. A.0.94s
2. B.0.96s
3. C.0.93s
4. D.0.95s
Show answer
Answer: B. 0.96s
AI explanation
1. Analyze the Question
We are given the altitude ( $h = 312\text{ m}$ ) and the temperature ( $T = -10.00^\circ\text{C}$ ). We need to find the time ( $t$ ) it takes for the sound to travel to the ground. To do this, we must first determine the velocity of sound at the given temperature.
2. Explain the Concept
The velocity of sound in air is dependent on temperature. The relationship is given by the formula:
$v_t = v_0 \sqrt{\frac{T_k}{T_0}}$
Where:
$v_t$ = velocity at temperature $T$
$v_0$ = velocity at $0^\circ\text{C}$ ( $331\text{ m/s}$ )
$T_k$ = absolute temperature in Kelvin ( $T^\circ\text{C} + 273$ )
$T_0$ = absolute temperature at $0^\circ\text{C}$ ( $273\text{ K}$ )
Alternatively, for small temperature changes, we use the approximation: $v_t \approx v_0 + 0.6T$ . However, using the absolute temperature formula is more precise for physics examinations.
3. Show the Solution
Step 1: Convert temperature to Kelvin $T_k = -10 + 273 = 263\text{ K}$
Step 2: Calculate the velocity of sound at $-10^\circ\text{C}$
$v_t = 331 \times \sqrt{\frac{263}{273}}$
$v_t = 331 \times \sqrt{0.96337}$
$v_t = 331 \times 0.9815$
$v_t \approx 324.88\text{ m/s}$
Step 3: Calculate the time taken Using the formula $t = \frac{\text{distance}}{\text{velocity}}$ :
$t = \frac{312}{324.88}$
$t \approx 0.9603\text{ s}$
Rounding to two decimal places, we get 0.96s.
4. Identify the Answer
Comparing our result to the options provided: A. 0.94s B. 0.96s C. 0.93s D. 0.95s
The calculated value matches option B.
5. Exam Tip
When dealing with sound velocity and temperature in JAMB, always remember that sound travels slower in colder air. If your calculated velocity is higher than $331\text{ m/s}$ when the temperature is below $0^\circ\text{C}$ , you know you have made a calculation error!
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23.
A generator manufacturing company accidentally made an AC generator instead of a DC generator. To fix this error,
1. A.the magnetic field needs to be made stronger
2. B.the split rings should be replaced with slip rings
3. C.the number of turns of the armature coil needs to be decreased
4. D.the slip rings should be replaced with split rings
Show answer
Answer: D. the slip rings should be replaced with split rings
AI explanation
Analysis of the Question
This question tests your understanding of the fundamental construction differences between an Alternating Current (AC) generator and a Direct Current (DC) generator. You are asked to identify the specific component change required to convert an AC output into a DC output.
Concept Explanation
AC Generator: Uses slip rings (two continuous metal rings). As the armature rotates, the current flows in one direction for half a turn and the opposite direction for the other half, resulting in an alternating current.
DC Generator: Uses a split-ring commutator (a single ring split into two halves). The split-ring commutator acts as a mechanical rectifier. As the coil rotates, the split rings reverse the connections to the external circuit at the exact moment the current in the coil reverses. This ensures that the current flowing through the external circuit always moves in the same direction, producing direct current.
Step-by-Step Solution
Identify the current setup: The company currently has an AC generator, which uses slip rings.
Identify the goal: The company wants a DC generator.
Determine the necessary change: To convert the output to DC, the alternating current must be rectified. This is achieved by replacing the slip rings (which maintain the alternating nature of the current) with a split-ring commutator.
Evaluate the options: • Option A (Magnetic field strength) affects the magnitude of the induced EMF, not the direction/type of current. • Option B (Slip rings) is what the generator already has; this would keep it as an AC generator. • Option C (Number of turns) affects the magnitude of the voltage, not the type of current. • Option D (Split rings) correctly identifies the component needed to rectify the current into DC.
Conclusion
Replacing the slip rings with a split-ring commutator is the standard engineering procedure to convert an AC generator into a DC generator.
Exam Tip: Remember the mnemonic "DC = Split" (Direct Current uses a Split-ring commutator) and "AC = Slip" (Alternating Current uses Slip rings). This simple trick will save you time in the exam hall!
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24.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
25.
The pinhole camera works on
1. A.the principle of the reversibility of light
2. B.the principle of the rectilinear propagation of light
3. C.Huygen’s principle
4. D.the principle of total internal reflection of light
Show answer
Answer: B. the principle of the rectilinear propagation of light
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26.
On a particular hot day, the temperature is 40°C and the partial pressure of water vapor in the air is 38.8 mmHg. What is the relative humidity?
1. A.70
2. B.62
3. C.80
4. D.42
Show answer
Answer: A. 70
AI explanation
1. Analyze the Question
We are asked to calculate the relative humidity of the air given the current temperature (40°C) and the actual partial pressure of water vapor (38.8 mmHg). To solve this, we need the Saturated Vapor Pressure (SVP) of water at 40°C.
2. Explain the Concept
Relative humidity is defined as the ratio of the actual partial pressure of water vapor in the air to the saturated vapor pressure of water at that same temperature, expressed as a percentage.
Formula:
$\text{Relative Humidity} = \left( \frac{\text{Actual Vapor Pressure}}{\text{Saturated Vapor Pressure at that temperature}} \right) \times 100\%$
Note: In physics problems of this nature, if the Saturated Vapor Pressure is not explicitly provided in the question text, it is usually retrieved from standard steam tables or provided in the exam's data sheet. At 40°C, the standard Saturated Vapor Pressure of water is approximately 55.3 mmHg.
3. Show the Solution
Actual Vapor Pressure: 38.8 mmHg
Saturated Vapor Pressure (at 40°C): 55.3 mmHg
Using the formula:
$\text{Relative Humidity} = \left( \frac{38.8}{55.3} \right) \times 100$
$\text{Relative Humidity} = 0.7016 \times 100$
$\text{Relative Humidity} \approx 70\%$
4. Identify the Answer
Comparing our result to the given options, the calculated value matches option A.
5. Exam Tip
When dealing with humidity questions in JAMB, always remember that the denominator (Saturated Vapor Pressure) must correspond to the temperature given in the question. If you ever forget the SVP values, look closely at the "Constants" or "Data" section usually provided at the beginning of the Physics exam booklet—they often hide the necessary values there!
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27.
How much work is done against the gravitational force on a 3.0 kg object when it is carried from the ground floor to the roof of a building, a vertical climb of 240 m?
1. A.7.2 kJ
2. B.4.6 kJ
3. C.6.8 kJ
4. D.8.4 kJ
Show answer
Answer: A. 7.2 kJ
AI explanation
Analysis
To solve this problem, we need to calculate the work done against gravity. In physics, when an object is lifted vertically, the work done is equal to the change in its gravitational potential energy.
Concept
The formula for work done ( $W$ ) against gravity is:
$W = m \times g \times h$
Where:
$m$ = mass of the object (in kg)
$g$ = acceleration due to gravity (standard value is $10 \, \text{m/s}^2$ for JAMB calculations, unless specified as $9.8 \, \text{m/s}^2$ )
$h$ = vertical height (in meters)
Solution
Step 1: Identify the given values.
Mass ( $m$ ) = $3.0 \, \text{kg}$
Height ( $h$ ) = $240 \, \text{m}$
Gravity ( $g$ ) = $10 \, \text{m/s}^2$
Step 2: Apply the formula.
$W = 3.0 \, \text{kg} \times 10 \, \text{m/s}^2 \times 240 \, \text{m}$
Step 3: Calculate the result.
$W = 30 \times 240$
$W = 7,200 \, \text{Joules}$
Step 4: Convert to kilojoules (kJ). Since $1,000 \, \text{J} = 1 \, \text{kJ}$ :
$7,200 \, \text{J} = 7.2 \, \text{kJ}$
Conclusion
Comparing our result to the given options, the correct value is $7.2 \, \text{kJ}$ .
Exam Tip
In JAMB Physics, always check if the question implies the use of $g = 10 \, \text{m/s}^2$ or $g = 9.8 \, \text{m/s}^2$ . If the options are round numbers, $10 \, \text{m/s}^2$ is almost always the intended value, as it makes calculations much faster and easier to perform without a calculator!
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28.
Which of the following statements regarding the application of electrical conduction via gases is/are correct? Electrical conduction in gas is applied in: (i) The identification of gases (ii) Lighting/fluorescent tubes (iii) Photocells (iv) Cathode ray oscilloscope/T.V. tubes
1. A.(i), (iii) and (iv) only
2. B.(i), (ii) and (iv) only
3. C.(ii), (iii) and (iv) only
4. D.(i), (ii) and (iii) only
Show answer
Answer: B. (i), (ii) and (iv) only
AI explanation
To solve this question, let’s break down each application of electrical conduction through gases:
1. Analysis of the Statements
(i) The identification of gases: This is correct. When a gas is subjected to a high-voltage discharge at low pressure, it emits a characteristic spectrum (spectral lines). By analyzing these lines (spectroscopy), scientists can identify the specific gas present.
(ii) Lighting/fluorescent tubes: This is correct. Fluorescent tubes and neon signs work by passing an electric current through a gas or vapor (like mercury vapor or neon). The gas becomes ionized, emits ultraviolet light, which then strikes a phosphor coating to produce visible light.
(iii) Photocells: This is incorrect in the context of electrical conduction through gases. Photocells (or photoelectric cells) operate based on the photoelectric effect, where light hitting a metal surface causes the emission of electrons. While some gas-filled photocells exist, the fundamental principle of a photocell is the interaction of light with a solid surface, not the conduction of electricity through a gas as the primary mechanism.
(iv) Cathode ray oscilloscope (CRO) / T.V. tubes: This is correct. These devices rely on the production of a beam of electrons in a vacuum or low-pressure gas environment. The movement of these electrons (cathode rays) is controlled by electric or magnetic fields to display images or waveforms.
2. Evaluating the Options
Based on our analysis, statements (i), (ii), and (iv) are the correct applications of electrical conduction through gases.
Option A includes (iii), which is incorrect.
Option B includes (i), (ii), and (iv), which matches our findings.
Option C includes (iii), which is incorrect.
Option D includes (iii), which is incorrect.
3. Conclusion
Exam Tip: When you see questions about "conduction through gases," always look for keywords like discharge tubes, ionization, spectral lines, or cathode rays. If you see "photoelectric effect," remember that it is primarily a surface phenomenon involving solid metals, not gas conduction.
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29.
A beam of light travelling in water is incident on a glass which is immersed in the water. The incident beam makes an angle of $40^o$ with the normal. Calculate the angle of refraction in the glass. [Refractive index of water = 1.33, Refractive index of glass = 1.5]
1. A. $29.36^o$
2. B. $25.37^o$
3. C. $37.21^o$
4. D. $34.75^o$
Show answer
Answer: D. $34.75^o$
AI explanation
1. Analyze the Question
We are given:
Medium 1 (Incident medium): Water ( $n_1 = 1.33$ )
Medium 2 (Refractive medium): Glass ( $n_2 = 1.5$ )
Angle of incidence ( $i$ ): $40^\circ$
We need to find the angle of refraction ( $r$ ).
2. Explain the Concept
To solve this, we use Snell’s Law of Refraction, which states:
$n_1 \sin(i) = n_2 \sin(r)$
Where:
$n_1$ is the refractive index of the first medium.
$i$ is the angle of incidence.
$n_2$ is the refractive index of the second medium.
$r$ is the angle of refraction.
3. Show the Solution
Step 1: Rearrange the formula to solve for $\sin(r)$ :
$\sin(r) = \frac{n_1 \sin(i)}{n_2}$
Step 2: Plug in the given values:
$\sin(r) = \frac{1.33 \times \sin(40^\circ)}{1.5}$
Step 3: Calculate $\sin(40^\circ)$ : Using a calculator, $\sin(40^\circ) \approx 0.6428$
Step 4: Perform the multiplication and division:
$\sin(r) = \frac{1.33 \times 0.6428}{1.5}$
$\sin(r) = \frac{0.8549}{1.5}$
$\sin(r) \approx 0.5699$
Step 5: Find the angle $r$ by taking the inverse sine ( $\sin^{-1}$ ):
$r = \sin^{-1}(0.5699)$
$r \approx 34.75^\circ$
4. Identify the Answer
Comparing our result to the options provided, the calculated angle matches option D.
5. Exam Tip
When dealing with refraction between two media that are not air, always remember to use the refractive index of the first medium ( $n_1$ ) instead of assuming it is 1. A common mistake students make is using $1 \times \sin(i) = n_2 \sin(r)$ , which is only true if the light is traveling from air or a vacuum. Always check the "incident medium" carefully!
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30.
Which of the following is an example of a couple?
1. A.All of the above.
2. B.The forces that are applied to the handle of a screwdriver when you twist it.
3. C.The forces that are applied to a cross wench to loosen or tighten the lug nuts on a wheel of a car.
4. D.The forces that are applied to the steering wheel of a car when you turn it.
Show answer
Answer: A. All of the above.
AI explanation
Analysis
A couple in physics is defined as a pair of forces that are equal in magnitude, opposite in direction, and act along parallel lines but not along the same straight line. The primary effect of a couple is to produce a turning effect (torque) without causing any linear acceleration.
Concept Explanation
To identify a couple, look for these three conditions:
Two forces: There must be two distinct forces acting on the object.
Equal and Opposite: The forces must be equal in magnitude and act in opposite directions.
Turning Effect: The forces must be applied at different points to create a rotation around a central pivot or axis.
Let's evaluate the examples provided:
Screwdriver: When you twist a screwdriver, your thumb and fingers exert two equal forces in opposite directions on opposite sides of the handle to create rotation. This is a classic example of a couple.
Cross Wrench: When loosening lug nuts, you push down on one arm of the wrench and pull up on the opposite arm. These two forces are equal, opposite, and parallel, creating a couple.
Steering Wheel: When turning a steering wheel, your hands are placed on opposite sides of the wheel, applying equal and opposite forces to rotate it. This is also a couple.
Solution
Since the screwdriver, the cross wrench, and the steering wheel all involve two equal, opposite, and parallel forces acting to produce a turning effect, they all qualify as examples of a couple. Therefore, "All of the above" is the correct classification.
Identification of the Answer
The correct option is A.
Exam Tip
Whenever you see a question about a "couple," think of rotation. If the action involves using two hands or two points of force to turn an object (like a tap, a steering wheel, or a wrench), you are dealing with a couple!
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31.
When a water droplet is placed on a freshly cut piece of wood, it spreads out to form a thin layer because the wood is
1. A.not at equilibrium with the water
2. B.cohesive to water
3. C.at equilibrium with the water
4. D.adhesive to water
Show answer
Answer: D. adhesive to water
AI explanation
1. Analyze the Question
The question asks why a water droplet spreads out into a thin layer when placed on a freshly cut piece of wood. We need to identify the physical force or property responsible for this behavior.
2. Explain the Concept
This phenomenon is governed by two fundamental forces in fluid mechanics:
Cohesion: This is the force of attraction between molecules of the same substance (e.g., water molecules sticking to other water molecules).
Adhesion: This is the force of attraction between molecules of different substances (e.g., water molecules sticking to the surface of the wood).
When a liquid spreads out on a surface (wetting the surface), it means the adhesive forces between the liquid and the solid surface are stronger than the cohesive forces within the liquid itself. If the cohesive forces were stronger, the water would bead up into a sphere to minimize contact with the surface.
3. Show the Solution
Step 1: Observe the behavior of the water. Since the water spreads into a thin layer, it is "wetting" the wood.
Step 2: Relate the behavior to the forces. Wetting occurs when the attraction between the water molecules and the wood molecules (adhesion) is greater than the attraction between the water molecules themselves (cohesion).
Step 3: Evaluate the options. • A & C: Equilibrium refers to a state of balance, which does not explain the spreading behavior. • B: If the wood were cohesive to water, it would imply the wood is pulling water molecules toward other water molecules, which is incorrect. • D: Because the wood attracts the water molecules, we describe the wood as being adhesive to the water.
4. Identify the Answer
The correct option is D. The wood is adhesive to the water, meaning the adhesive forces between the wood and water are strong enough to overcome the cohesive forces of the water, causing it to spread.
5. Tip
Memory Trick: Think of Adhesion as Attraction between Another substance and the liquid. Think of Cohesion as Connection between the Came (same) substance. If the liquid spreads, Adhesion wins!
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32.
Which process is responsible for production of energy in stars?
1. A.Nuclear reaction
2. B.Nuclear fission
3. C.Nuclear fusion
4. D.Radioactive decay
Show answer
Answer: C. Nuclear fusion
AI explanation
Analysis
The question asks for the specific physical process that powers stars, including our Sun. We need to distinguish between different types of nuclear processes to identify which one occurs under the extreme conditions found in stellar cores.
Concept Explanation
To understand how stars produce energy, we look at Nuclear Physics:
Nuclear Fission: This is the process where a heavy, unstable nucleus (like Uranium-235) splits into smaller, lighter nuclei, releasing energy. This is the principle used in nuclear power plants and atomic bombs.
Nuclear Fusion: This is the process where two light atomic nuclei (typically hydrogen isotopes like deuterium and tritium) combine or "fuse" together under immense heat and pressure to form a heavier nucleus (like helium). This process releases a massive amount of energy according to Einstein’s mass-energy equivalence principle ( $E = mc^2$ ).
Radioactive Decay: This is the spontaneous breakdown of an atomic nucleus resulting in the release of energy and matter from the nucleus. While it occurs in stars, it is not the primary source of their massive energy output.
Step-by-Step Solution
Step 1: Identify the conditions in a star. Stars have extremely high temperatures and pressures at their cores.
Step 2: Evaluate the processes. The high temperature and pressure are sufficient to overcome the electrostatic repulsion between positively charged protons, allowing them to collide and fuse.
Step 3: Compare the processes. While "Nuclear reaction" (Option A) is a broad term that includes fusion, "Nuclear fusion" (Option C) is the specific, scientifically accurate process responsible for stellar energy production.
Step 4: Conclusion. Because stars fuse hydrogen atoms into helium, the correct process is nuclear fusion.
Identification of the Answer
The correct option is C.
Exam Tip
When you see questions about energy in stars, always look for the word "Fusion". A simple way to remember it is: Fusion = Fuse together (making something bigger), while Fission = Fissure/Split (making something smaller).
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33.
A parallel plate capacitor separated by an air gap is made of $0.8m^2$ tin plates and 20 mm apart. It is connected to 120 V battery. What is the charge on each plate? Take $ε_o$ = $8.85×10^-12 Fm^-1$
1. A.3.54nC
2. B.42.5nC
3. C.35.4nC
4. D.4.25nC
Show answer
Answer: B. 42.5nC
AI explanation
1. Analyze the question
We are asked to calculate the charge ( $Q$ ) stored on the plates of a parallel plate capacitor. We are given:
Area of plates ( $A$ ) = $0.8 \, \text{m}^2$
Distance between plates ( $d$ ) = $20 \, \text{mm} = 0.02 \, \text{m}$
Voltage ( $V$ ) = $120 \, \text{V}$
Permittivity of free space ( $\varepsilon_o$ ) = $8.85 \times 10^{-12} \, \text{Fm}^{-1}$
2. Explain the concept
To find the charge, we use two fundamental formulas for capacitors:
Capacitance ( $C$ ): For a parallel plate capacitor, $C = \frac{\varepsilon_o A}{d}$
Charge ( $Q$ ): The relationship between charge, capacitance, and voltage is $Q = C \times V$
By combining these, we get: $Q = \frac{\varepsilon_o A V}{d}$
3. Show the solution
Step 1: Convert units to SI units
$d = 20 \, \text{mm} = 20 \times 10^{-3} \, \text{m} = 0.02 \, \text{m}$
Step 2: Calculate the Capacitance ( $C$ )
$C = \frac{8.85 \times 10^{-12} \times 0.8}{0.02}$
$C = \frac{7.08 \times 10^{-12}}{0.02}$
$C = 354 \times 10^{-12} \, \text{F} = 354 \, \text{pF}$
Step 3: Calculate the Charge ( $Q$ )
$Q = C \times V$
$Q = (354 \times 10^{-12}) \times 120$
$Q = 42,480 \times 10^{-12} \, \text{C}$
$Q = 4.248 \times 10^{-8} \, \text{C}$
To express this in nanoCoulombs (nC), where $1 \, \text{nC} = 10^{-9} \, \text{C}$ :
$Q \approx 42.5 \times 10^{-9} \, \text{C} = 42.5 \, \text{nC}$
4. Identify the answer
Comparing our result to the options provided, the correct value is 42.5 nC. This matches option B.
5. Tip
When dealing with capacitors, always ensure your distance ( $d$ ) is in meters and your area ( $A$ ) is in square meters before plugging them into the formula. A common mistake in JAMB exams is forgetting to convert millimeters (mm) to meters (m), which leads to a calculation error by a factor of 1000!
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34.
The surface temperature of a swimming pool on a warm day is 25ºC and the temperature at the bottom is 15ºC. If the swimming pool has a surface area of 620 $m^2$ and a depth of 1.5m. Find the rate at which energy is transferred by conduction from the surface to the bottom of the swimming pool. [Thermal conductivity of water (k) = 0.6071 Wm-1K-1]
1. A.2.5kw
2. B.250kw
3. C.300kw
4. D.3.0kw
Show answer
Answer: A. 2.5kw
AI explanation
Analysis
To solve this problem, we need to calculate the rate of heat transfer (heat flow) through a liquid medium (water) due to conduction. We are given the temperature difference, the surface area, the thickness (depth), and the thermal conductivity of the material.
Concept
The rate of heat transfer by conduction is governed by Fourier’s Law of Heat Conduction, which is expressed by the formula:
$Q/t = \frac{kA(T_2 - T_1)}{d}$
Where:
$Q/t$ = Rate of heat transfer (Power in Watts)
$k$ = Thermal conductivity ( $0.6071 \, \text{Wm}^{-1}\text{K}^{-1}$ )
$A$ = Surface area ( $620 \, \text{m}^2$ )
$T_2 - T_1$ = Temperature difference ( $25^\circ\text{C} - 15^\circ\text{C} = 10 \, \text{K}$ )
$d$ = Depth/thickness ( $1.5 \, \text{m}$ )
Solution
Step 1: Identify the given values.
$k = 0.6071 \, \text{Wm}^{-1}\text{K}^{-1}$
$A = 620 \, \text{m}^2$
$\Delta T = 25 - 15 = 10 \, \text{K}$
$d = 1.5 \, \text{m}$
Step 2: Substitute the values into the formula.
$Q/t = \frac{0.6071 \times 620 \times 10}{1.5}$
Step 3: Perform the calculation.
Numerator: $0.6071 \times 620 \times 10 = 3764.02$
Divide by depth: $3764.02 / 1.5 = 2509.346 \, \text{W}$
Step 4: Convert to kilowatts (kW). Since $1000 \, \text{W} = 1 \, \text{kW}$ :
$2509.346 \, \text{W} \approx 2.509 \, \text{kW}$
Rounding to the nearest significant value provided in the options, we get 2.5 kW.
Conclusion
Comparing our result to the options provided, the calculated value matches option A.
Exam Tip
When solving heat transfer problems, always ensure your temperature difference is in Kelvin. However, because the formula uses the difference in temperature ( $\Delta T$ ), a difference of $10^\circ\text{C}$ is exactly the same as a difference of $10 \, \text{K}$ , so you don't need to convert the individual temperatures to Kelvin first!
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35.
In an AC circuit, resonance occurs when the impedance of the circuit is:
1. A.Zero
2. B.Maximum
3. C.Equal to the capacitive reactance of the circuit
4. D.Minimum
Show answer
Answer: D. Minimum
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36.
Which of the following thermometers measures temperature from the thermal radiation emitted by objects?
1. A.Pyrometer thermometer
2. B.Platinum resistance thermometer
3. C.Thermocouple thermometer
4. D.Constant pressure gas thermometer
Show answer
Answer: A. Pyrometer thermometer
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37.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
38.
A metal sphere is placed on an insulating stand. A negatively charged rod is brought close to it. If the sphere is earthed and the rod is taken away, what will be the charge on the sphere?
1. A.The sphere will remain neutral.
2. B.The sphere will have a net negative charge.
3. C.The sphere will have a net positive charge.
4. D.The sphere will become polarized
Show answer
Answer: C. The sphere will have a net positive charge.
AI explanation
Analysis of the Question
This question tests your understanding of electrostatic induction and the process of charging by induction. You are asked to determine the final state of a metal sphere after it undergoes a specific sequence of interactions with a charged rod and an earth connection.
Concept Explanation: Charging by Induction
Charging by induction allows you to charge an object without touching it with a charged body. Here is the step-by-step physical process:
Induction: When a negatively charged rod is brought near the neutral metal sphere, the free electrons in the sphere are repelled to the far side of the sphere. This leaves the side near the rod with a net positive charge.
Earthing: When you connect the sphere to the earth (grounding), the repelled electrons (which are on the far side) flow into the earth because they are repelled by the rod and have a path to escape.
Breaking the Earth Connection: If you remove the earth connection while the rod is still held close, the sphere is now "trapped" with a deficiency of electrons.
Removing the Rod: Once the rod is taken away, the remaining positive charges redistribute themselves uniformly over the surface of the sphere.
Step-by-Step Solution
Step 1: The negatively charged rod is brought near the sphere. The sphere polarizes: positive charges gather near the rod, and negative charges are pushed to the opposite side.
Step 2: The sphere is earthed. The excess negative charges (electrons) on the far side flow into the earth.
Step 3: The earth connection is removed. The sphere is now left with a net positive charge because electrons have left the sphere.
Step 4: The rod is removed. The sphere remains positively charged.
Conclusion
Because electrons were removed from the sphere through the earthing process, the sphere is left with a deficit of electrons, which means it acquires a net positive charge.
Exam Tip: Always remember the "Opposite Rule" in induction: When charging by induction, the object being charged will always acquire a charge opposite to that of the inducing rod. Since the rod was negative, the sphere must become positive!
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39.
The half life of a radioactive material is 12 days. Calculate the decay constant.
1. A.0.8663 $day^{-1}$
2. B.0.04331 $day^{-1}$
3. C.0.17325 $day^{-1}$
4. D.0.05775 $day^{-1}$
Show answer
Answer: D. 0.05775 $day^{-1}$
AI explanation
1. Analyze the question
We are given the half-life ( $T_{1/2}$ ) of a radioactive material as 12 days, and we are asked to calculate the decay constant ( $\lambda$ ).
2. Explain the concept
In radioactivity, the half-life ( $T_{1/2}$ ) is the time required for half of the radioactive nuclei in a sample to decay. The relationship between the half-life and the decay constant ( $\lambda$ ) is given by the formula:
$T_{1/2} = \frac{\ln(2)}{\lambda}$
Where:
$T_{1/2} = 12 \text{ days}$
$\ln(2) \approx 0.693$
To find the decay constant ( $\lambda$ ), we rearrange the formula:
$\lambda = \frac{0.693}{T_{1/2}}$
3. Show the solution
Step 1: Identify the given values. $T_{1/2} = 12 \text{ days}$
Step 2: Use the formula for the decay constant. $\lambda = \frac{0.693}{12}$
Step 3: Perform the division. $\lambda = 0.05775 \text{ day}^{-1}$
4. Identify the answer
Comparing our result with the provided options: A. 0.8663 B. 0.04331 C. 0.17325 D. 0.05775
The calculated value matches option D.
5. Tip
When dealing with radioactivity problems in JAMB, always remember that $\ln(2)$ is approximately 0.693. If you ever forget the formula, just remember that the decay constant and half-life are inversely proportional—as one increases, the other decreases. Also, ensure your units are consistent (if the half-life is in days, your decay constant must be in $day^{-1}$ ).
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40.
An object is placed 35 cm away from a convex mirror with a focal length of magnitude 15 cm. What is the location of the image?
1. A.26.25 cm behind the mirror
2. B.10.5 cm behind the mirror
3. C.26.25 cm in front of the mirror
4. D.10.5 cm in front of the mirror
Show answer
Answer: B. 10.5 cm behind the mirror
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41.
The branch of physics that deals with the motion of objects and the forces acting on them is called:
1. A.Electromagnetism
2. B.Thermodynamics
3. C.Mechanics
4. D.Quantum mechanics
Show answer
Answer: C. Mechanics
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42.
The pitch of a musical note is determined by the frequency of the sound wave that it produces. If two instruments have the same frequency, which of the following factors will most affect the difference in their pitches?
1. A.The shape of the instrument
2. B.The tension of the string
3. C.The size of the instrument
4. D.The material of the instrument
Show answer
Answer: C. The size of the instrument
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43.
How much net work is required to accelerate a 1200 kg car from 10 $ms^{-1}$ to 15 $ms^{-1}$
1. A.1.95× $10^5 j$
2. B.1.35× $10^4 j$
3. C.7.5× $10^4 j$
4. D.6.0× $10^4 j$
Show answer
Answer: C. 7.5× $10^4 j$
AI explanation
Analysis
To solve this problem, we use the Work-Energy Theorem. This theorem states that the net work done on an object is equal to the change in its kinetic energy.
Concept
The kinetic energy ( $K.E.$ ) of an object is given by the formula:
$K.E. = \frac{1}{2}mv^2$
The net work done ( $W$ ) to change the velocity of an object from an initial velocity ( $u$ ) to a final velocity ( $v$ ) is:
$W = \Delta K.E. = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$
$W = \frac{1}{2}m(v^2 - u^2)$
Solution
Given data:
Mass ( $m$ ) = $1200\text{ kg}$
Initial velocity ( $u$ ) = $10\text{ ms}^{-1}$
Final velocity ( $v$ ) = $15\text{ ms}^{-1}$
Step 1: Calculate the change in the square of the velocities.
$v^2 - u^2 = (15)^2 - (10)^2$
$v^2 - u^2 = 225 - 100 = 125$
Step 2: Apply the work formula.
$W = \frac{1}{2} \times 1200 \times 125$
$W = 600 \times 125$
$W = 75,000\text{ J}$
Step 3: Convert to standard form.
$75,000 = 7.5 \times 10^4\text{ J}$
Comparing this result to the given options, it matches option C.
Tip
When solving "Work-Energy" problems, always check if you are asked for the total work or the net work. If the question mentions a change in speed, the Work-Energy Theorem is almost always the fastest way to the answer. Avoid calculating acceleration and distance using equations of motion unless absolutely necessary, as it takes much longer and increases the chance of a calculation error!
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44.
What is the name of the model of the atom that describes electrons as orbiting the nucleus in specific energy levels?
1. A.Bohr model
2. B.Dalton model
3. C.Rutherford model
4. D.Thomson model
Show answer
Answer: A. Bohr model
AI explanation
Analysis
The question asks for the specific atomic model that introduced the concept of electrons occupying fixed, quantized energy levels (or shells) while orbiting the nucleus.
Concept Explanation
To understand this, let's look at the evolution of the atomic model:
Thomson Model ("Plum Pudding"): Proposed that the atom is a sphere of positive charge with electrons embedded in it like plums in a pudding. It did not feature a nucleus.
Rutherford Model ("Planetary Model"): Proposed that the atom has a small, dense, positively charged nucleus with electrons orbiting it like planets around the sun. However, it failed to explain why electrons didn't lose energy and spiral into the nucleus.
Bohr Model: Niels Bohr refined Rutherford's model by proposing that electrons can only exist in specific, stable energy levels (orbits) without radiating energy. Electrons can only move between these levels by absorbing or emitting specific amounts of energy (quanta).
Dalton Model: The earliest model, which viewed the atom as a solid, indivisible sphere.
Step-by-Step Solution
Step 1: Evaluate the options based on the "energy levels" requirement.
Step 2: Recognize that while Rutherford introduced the nucleus, he did not define the quantized energy levels.
Step 3: Identify that the Bohr model specifically addresses the stability of the atom by restricting electrons to fixed orbits with defined energy values.
Step 4: Conclude that the Bohr model is the correct description for electrons in specific energy levels.
Conclusion
The Bohr model is the correct answer as it successfully introduced the concept of stationary states (energy levels) to explain atomic stability and spectral lines.
Exam Tip: Remember the mnemonic "Bohr = Levels". Whenever you see a question about "energy levels," "shells," or "quantized orbits," the answer is almost always the Bohr model.
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45.
A relative density bottle has a mass of 19 g when empty. When it is completely filled with water, its mass is 66 g. What will be its mass if completely filled with alcohol of relative density 0.8?
1. A.47 g
2. B.52.8 g
3. C.37.6 g
4. D.56.6 g
Show answer
Answer: D. 56.6 g
AI explanation
Analysis
To solve this problem, we need to understand the relationship between mass, volume, and relative density. The relative density of a substance is the ratio of the mass of a certain volume of that substance to the mass of an equal volume of water.
Concept
Mass of water: The mass of the water alone is the total mass when filled with water minus the mass of the empty bottle.
Volume: Since the bottle is the same, the volume of alcohol will be equal to the volume of water.
Relative Density (R.D.): $ $\text{R.D.} = \frac{\text{Mass of substance}}{\text{Mass of equal volume of water}}$ $Therefore,$ \text{Mass of substance} = \text{R.D.} \times \text{Mass of equal volume of water}$.
Step-by-Step Solution
Step 1: Calculate the mass of the water.
Mass of empty bottle = $19\text{ g}$
Mass of bottle + water = $66\text{ g}$
Mass of water = $66\text{ g} - 19\text{ g} = 47\text{ g}$
Step 2: Calculate the mass of the alcohol.
Relative density of alcohol = $0.8$
Mass of alcohol = $\text{R.D. of alcohol} \times \text{Mass of water}$
Mass of alcohol = $0.8 \times 47\text{ g} = 37.6\text{ g}$
Step 3: Calculate the total mass of the bottle filled with alcohol.
Total mass = Mass of empty bottle + Mass of alcohol
Total mass = $19\text{ g} + 37.6\text{ g} = 56.6\text{ g}$
Conclusion
Comparing our result to the options provided, we see that $56.6\text{ g}$ corresponds to option D.
Exam Tip
Always remember to subtract the mass of the container (the "tare" weight) before performing calculations involving the density of the contents. Many students mistakenly multiply the total mass ( $66\text{ g}$ ) by the relative density, which leads to an incorrect answer. Always isolate the mass of the liquid first!
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46.
Which of the following is NOT an example of elementary modern physics?
1. A.Classical mechanics
2. B.Quantum mechanics
3. C.Special relativity
4. D.Nuclear physics
Show answer
Answer: A. Classical mechanics
AI explanation
Analysis
The question asks us to identify which of the listed branches of physics does not fall under the category of "modern physics." In physics, we generally divide the subject into two broad eras: Classical Physics and Modern Physics.
Concept Explanation
Classical Physics: This refers to the laws of physics developed before the 20th century. It includes Newtonian mechanics (classical mechanics), thermodynamics, and electromagnetism. These theories work perfectly for objects moving at speeds much slower than the speed of light and for macroscopic objects (things we can see).
Modern Physics: This refers to the revolutionary theories developed from the early 20th century onwards, primarily to explain phenomena that classical physics could not account for. This includes: • Quantum Mechanics: Deals with the behavior of matter and energy at the atomic and subatomic levels. • Special Relativity: Deals with objects moving at speeds approaching the speed of light. • Nuclear Physics: Deals with the constituents and interactions of atomic nuclei.
Step-by-Step Solution
Evaluate Option A (Classical mechanics): This is the study of motion based on Newton’s laws. It was established in the 17th century and is the foundation of classical physics, not modern physics.
Evaluate Option B (Quantum mechanics): This is a cornerstone of modern physics, developed to explain the behavior of particles at the microscopic scale.
Evaluate Option C (Special relativity): Proposed by Albert Einstein in 1905, this is a fundamental pillar of modern physics.
Evaluate Option D (Nuclear physics): This field emerged in the 20th century following the discovery of the atom's structure and radioactivity, making it a key part of modern physics.
Since Classical mechanics belongs to the pre-20th-century era, it is the correct answer.
Conclusion
Exam Tip: Remember the "1900" rule. If a theory was primarily developed to explain things that happen at the speed of light or at the scale of atoms (post-1900), it is "Modern Physics." If it deals with everyday objects (like balls, cars, or planets) using Newton's laws, it is "Classical Physics."
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47.
The number of holes in an intrinsic semiconductor
1. A.is not equal to the number of free electrons
2. B.is greater than the number of free electrons
3. C.is equal to the number of free electrons
4. D.is less than the number of free electrons
Show answer
Answer: C. is equal to the number of free electrons
AI explanation
Analysis
This question tests your understanding of the fundamental properties of intrinsic semiconductors (pure semiconductors like Silicon or Germanium) at thermal equilibrium.
Concept Explanation
An intrinsic semiconductor is a pure material with no significant dopant impurities.
Generation: When thermal energy is applied to an intrinsic semiconductor, electrons gain enough energy to break their covalent bonds and move into the conduction band, leaving behind a "hole" in the valence band.
Pair Production: This process is called electron-hole pair generation. Because every time an electron is promoted to the conduction band, exactly one hole is created in the valence band, the rate of electron generation is equal to the rate of hole generation.
Equilibrium: In an intrinsic semiconductor, the concentration of free electrons ( $n$ ) is always equal to the concentration of holes ( $p$ ). Mathematically, this is expressed as: $ $n = p = n_i$ $where$ n_i$ is the intrinsic carrier concentration.
Step-by-Step Solution
Identify the material: The question specifies an intrinsic semiconductor.
Apply the principle: In pure (intrinsic) semiconductors, charge carriers are created only by thermal excitation.
Relate the carriers: Since each excitation creates one free electron and one hole simultaneously, the number of free electrons must equal the number of holes.
Evaluate the options: • A is incorrect because they are equal. • B is incorrect because holes do not outnumber electrons in an intrinsic material. • C is correct because $n = p$ . • D is incorrect because electrons do not outnumber holes in an intrinsic material.
Conclusion
In an intrinsic semiconductor, the number of holes is exactly equal to the number of free electrons because they are generated in pairs.
Exam Tip: If the semiconductor were extrinsic (doped), this would change! In an n-type semiconductor, electrons are the majority carriers, and in a p-type semiconductor, holes are the majority carriers. Always check if the question says "intrinsic" or "doped."
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48.
A travelling wave of amplitude 0.80 m has a frequency of 16 Hz and a wave speed of 20 $ms^{-1}$ Calculate the wave number of the wave.
1. A.3
2. B.4
3. C.5
4. D.2
Show answer
Answer: C. 5
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49.
Which of the following types of electromagnetic waves is used in night vision goggles?
1. A.Microwaves
2. B.Ultraviolet waves
3. C.Infrared waves
4. D.Radio waves
Show answer
Answer: C. Infrared waves
AI explanation
Analysis
The question asks for the specific type of electromagnetic radiation utilized by night vision technology to allow humans to see in low-light or dark conditions.
Concept Explanation
Electromagnetic waves are categorized by their wavelengths and frequencies. Infrared (IR) radiation lies just beyond the red end of the visible light spectrum.
All objects with a temperature above absolute zero emit thermal radiation. Humans, animals, and warm objects emit significant amounts of infrared energy. Night vision goggles work by detecting this thermal radiation (heat) rather than relying on visible light. The goggles capture the infrared light emitted by objects and convert it into an electronic signal, which is then displayed as a visible image on a screen.
Step-by-Step Solution
Evaluate the options: • A. Microwaves: Primarily used for communication (Wi-Fi, satellite) and heating food. They are not used for thermal imaging. • B. Ultraviolet waves: These have shorter wavelengths than visible light and are often used for sterilization or detecting counterfeit currency, not for night vision. • C. Infrared waves: These are associated with heat. Since night vision is based on detecting the heat signatures of objects in the dark, this is the correct application. • D. Radio waves: These have the longest wavelengths and are used for broadcasting radio and television signals.
Conclusion: Because night vision technology relies on detecting thermal signatures (heat) emitted by objects, it specifically utilizes the infrared portion of the electromagnetic spectrum.
Correct Answer
The correct option is C.
Exam Tip
Think of "Infrared" as "Below Red." Since it is invisible to the human eye but carries heat, remember the mnemonic: "Heat = Infrared." Whenever you see a question about night vision, thermal cameras, or remote controls, the answer is almost always Infrared!
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50.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
51.
An air bubble of radius 4.5 cm initially at a depth of 12 m below the water surface rises to the surface. If the atmospheric pressure is equal to 10.34 m of water, the radius of the bubble just before it reaches the water surface is
1. A.6.43 cm
2. B.8.24 cm
3. C.4.26 cm
4. D.5.82 cm
Show answer
Answer: D. 5.82 cm
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52.
A lorry accelerates uniformly in a straight line with acceleration of $4ms^-2$ and covers a distance of 250 m in a time interval of 10 s. How far will it travel in the next 10 s?
1. A.650
2. B.900
3. C.800
4. D.250
Show answer
Answer: A. 650
AI explanation
1. Analyze the Question
We are given the acceleration ( $a = 4 \, \text{ms}^{-2}$ ) and the distance covered in the first 10 seconds ( $s_1 = 250 \, \text{m}$ ). We need to find the distance covered in the next 10 seconds.
2. Explain the Concept
To solve this, we use the equations of motion for uniform acceleration:
$s = ut + \frac{1}{2}at^2$
$v = u + at$
Where:
$u$ = initial velocity
$v$ = final velocity
$a$ = acceleration
$t$ = time
$s$ = distance
3. Show the Solution
Step 1: Find the initial velocity ( $u$ ) using the first interval. Given: $s_1 = 250 \, \text{m}$ , $t_1 = 10 \, \text{s}$ , $a = 4 \, \text{ms}^{-2}$ . Using $s = ut + \frac{1}{2}at^2$ : $250 = u(10) + \frac{1}{2}(4)(10)^2$ $250 = 10u + 2(100)$ $250 = 10u + 200$ $50 = 10u$ $u = 5 \, \text{ms}^{-1}$
Step 2: Find the velocity at the end of the first 10 seconds ( $v_1$ ). This will be the initial velocity for the next 10 seconds. $v_1 = u + at_1$ $v_1 = 5 + (4)(10)$ $v_1 = 5 + 40 = 45 \, \text{ms}^{-1}$
Step 3: Calculate the distance covered in the next 10 seconds ( $s_2$ ). For this interval, the initial velocity is $u_2 = 45 \, \text{ms}^{-1}$ , $t_2 = 10 \, \text{s}$ , and $a = 4 \, \text{ms}^{-2}$ . $s_2 = u_2t_2 + \frac{1}{2}at_2^2$ $s_2 = (45)(10) + \frac{1}{2}(4)(10)^2$ $s_2 = 450 + 2(100)$ $s_2 = 450 + 200$ $s_2 = 650 \, \text{m}$
4. Identify the Answer
The distance traveled in the next 10 seconds is 650 m. This matches option A.
5. Exam Tip
When a question asks for the distance in the "next" time interval, always remember that the final velocity of the first interval becomes the initial velocity for the second interval. Don't make the mistake of using the original starting velocity for the second part of the journey!
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53.
A positively charged particle is placed near a negatively charged particle. What is the direction of the electric force between the two particles?
1. A.The electric force is directed from the negative particle to the positive particle.
2. B.The electric force is zero.
3. C.The direction of the electric force cannot be determined.
4. D.The electric force is directed from the positive particle to the negative particle.
Show answer
Answer: D. The electric force is directed from the positive particle to the negative particle.
AI explanation
1. Analyze the question
The question asks for the direction of the electric force exerted between two particles with opposite charges (one positive and one negative).
2. Explain the concept
In electrostatics, the fundamental principle governing the interaction between charges is:
Like charges repel: Two positive charges or two negative charges push each other away.
Unlike charges attract: A positive charge and a negative charge pull each other toward one another.
The electric force is a vector quantity, meaning it has both magnitude and direction. By convention, the electric field lines originate from a positive charge and terminate at a negative charge. Similarly, the force of attraction between two opposite charges acts along the line joining them, pulling the positive charge toward the negative one and the negative charge toward the positive one.
3. Show the solution
Step 1: Identify the nature of the interaction. Since one particle is positive and the other is negative, they will experience an attractive force.
Step 2: Determine the direction of the force. The force on the positive particle is directed toward the negative particle, and the force on the negative particle is directed toward the positive particle.
Step 3: Evaluate the options. Option D describes the force as being directed from the positive particle to the negative particle. This aligns with the standard convention of electric field direction and the vector of attraction between the two points.
4. Identify the answer
The correct option is D.
Note: While the force is mutual (both particles pull on each other), in the context of physics problems regarding the direction of the electric field or the force vector between two opposite charges, we describe the direction as moving from the source (positive) to the sink (negative).
5. Exam Tip
Memory Trick: Think of the positive charge as the "giver" and the negative charge as the "receiver." Electric field lines and the resulting attractive force vectors always point from the "giver" (positive) to the "receiver" (negative).
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54.
Which of the following is a type of wave that is both mechanical and longitudinal?
1. A.Water waves
2. B.Seismic waves
3. C.Sound waves
4. D.Light waves
Show answer
Answer: C. Sound waves
AI explanation
1. Analyze the question
The question asks us to identify a wave that possesses two specific characteristics:
Mechanical: It requires a material medium (solid, liquid, or gas) to propagate.
Longitudinal: The particles of the medium vibrate parallel to the direction of wave propagation.
2. Explain the concept
Mechanical waves: These waves need a medium to travel. Without particles to vibrate (like in a vacuum), they cannot exist. Examples include sound and water waves.
Electromagnetic waves: These do not need a medium and can travel through a vacuum. Examples include light, X-rays, and radio waves.
Longitudinal waves: In these waves, the particles move back and forth in the same direction the energy is traveling (creating compressions and rarefactions).
Transverse waves: In these waves, the particles move perpendicular (at a 90-degree angle) to the direction of the wave.
3. Show the solution
Let’s evaluate the options:
A. Water waves: These are a combination of longitudinal and transverse motion (surface waves). They are mechanical, but not purely longitudinal.
B. Seismic waves: These include both P-waves (longitudinal) and S-waves (transverse). Because they are a mix, they are not the best fit for a general classification.
C. Sound waves: Sound is produced by vibrations that create regions of high pressure (compressions) and low pressure (rarefactions) in a medium. Because the air molecules move back and forth in the same direction the sound is traveling, it is longitudinal. Since sound cannot travel through a vacuum, it is mechanical.
D. Light waves: Light is an electromagnetic wave. It is transverse and does not require a medium.
4. Identify the answer
Sound waves perfectly fit the criteria of being both mechanical (requiring a medium) and longitudinal (vibrating parallel to the direction of travel).
5. Exam Tip
Remember the acronym "SLM" for Sound = Longitudinal = Mechanical. Conversely, remember that all electromagnetic waves (like light) are transverse and do not need a medium.
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55.
Which of the following statements is correct about the angle of dip at various points on Earth?
1. A.The angle of dip is zero at the equator and 90 degrees at the magnetic poles.
2. B.The angle of dip is greater at higher altitudes than at lower altitudes
3. C.The angle of dip is positive in the northern hemisphere and negative in the southern hemisphere.
4. D.The angle of dip is constant at all points on Earth
Show answer
Answer: A. The angle of dip is zero at the equator and 90 degrees at the magnetic poles.
AI explanation
Analysis of the Question
This question tests your understanding of Terrestrial Magnetism, specifically the concept of the Angle of Dip (or Inclination). The angle of dip is the angle that the Earth's magnetic field lines make with the horizontal surface of the Earth.
Concept Explanation
The Earth acts like a giant bar magnet. Because of this, the magnetic field lines are not parallel to the ground everywhere:
At the Magnetic Equator: The magnetic field lines are parallel to the Earth's surface. Since the field lines are horizontal, the angle they make with the horizontal is 0°.
At the Magnetic Poles: The magnetic field lines point directly into (or out of) the Earth's surface (vertically). Therefore, the angle they make with the horizontal is 90°.
Between the Equator and the Poles: The angle of dip varies between 0° and 90° depending on your latitude.
Step-by-Step Solution
Evaluate Option A: As explained above, at the equator, the magnetic field is horizontal (0° dip), and at the poles, it is vertical (90° dip). This matches the physical behavior of Earth's magnetic field.
Evaluate Option B: The angle of dip is primarily a function of latitude, not altitude. This statement is incorrect.
Evaluate Option C: While the dip direction changes, the standard definition of the angle of dip is the magnitude of the angle from the horizontal. It is not defined by a simple positive/negative sign convention across hemispheres in this context.
Evaluate Option D: We know the angle changes from 0° at the equator to 90° at the poles, so it is definitely not constant.
Conclusion
Based on the principles of geomagnetism, the angle of dip is 0° at the magnetic equator and increases to 90° as you move toward the magnetic poles.
Exam Tip: Think of a compass needle. If you were at the magnetic equator, a perfectly balanced compass needle would stay perfectly horizontal. If you were at the North Pole, the needle would try to point straight down into the ground! This visual helps you remember that the dip is 0° at the equator and 90° at the poles.
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56.
What is the amount of heat required to raise the temperature of a 0.02 kg of ice cube from $-10^oC$ to $10^oC$ ? [specific latent heat of fusion of ice = 3.34 x $10^5$ $Jkg^-1$ , Specific heat capacity of water = 4200 $Jkg^-1$ $k^-1$ Specific heat capacity of ice = 2100 $Jkg^-1$ $k^-1$
1. A.6680 J
2. B.1680 J
3. C.7520 J
4. D.7940 J
Show answer
Answer: D. 7940 J
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57.
Which of the following is/are not true about the heat capacity of a substance? (i) It is an intensive property (ii) Its S.I unit is $jK-1$ (iii) It is an extensive property (iv) Its S.I unit is $jkg-1$
1. A.(i) and (iii) only
2. B.(i), (ii) and (iv) only
3. C.(i) and (iv) only
4. D.(ii) and (iii) only
Show answer
Answer: C. (i) and (iv) only
AI explanation
To solve this question, we need to understand the definition and properties of Heat Capacity.
1. Analyze the Concepts
Heat Capacity ( $C$ ): This is the amount of heat required to raise the temperature of a body by one degree Celsius (or Kelvin). It is defined by the formula: $Q = C\Delta\theta$ , where $Q$ is heat energy and $\Delta\theta$ is the change in temperature.
Intensive vs. Extensive Properties: • Extensive properties depend on the amount of matter in the substance (e.g., mass, volume, heat capacity). If you have more of a substance, it takes more heat to raise its temperature. • Intensive properties do not depend on the amount of matter (e.g., density, specific heat capacity).
S.I. Units: • Since $C = \frac{Q}{\Delta\theta}$ , the unit is $\frac{\text{Joules}}{\text{Kelvin}}$ , which is written as $JK^{-1}$ . • $Jkg^{-1}$ is the unit for Specific Latent Heat, not Heat Capacity.
2. Evaluate the Statements
(i) It is an intensive property: False. Heat capacity depends on the mass of the object, making it an extensive property.
(ii) Its S.I unit is $JK^{-1}$ : True. As derived from the formula $C = \frac{Q}{\Delta\theta}$ .
(iii) It is an extensive property: True. Because it depends on the quantity of the substance.
(iv) Its S.I unit is $Jkg^{-1}$ : False. This is not the unit for heat capacity.
3. Identify the "Not True" Statements
The question asks for the statements that are not true. Based on our evaluation:
Statement (i) is not true.
Statement (iv) is not true.
Therefore, (i) and (iv) are the statements that are not true.
4. Conclusion
Comparing our findings with the given options, the correct choice is C.
Exam Tip: Always distinguish between Heat Capacity (which depends on the whole object) and Specific Heat Capacity (which is a property of the material itself and is intensive). Remember: "Specific" usually means "per unit mass," which makes it intensive!
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58.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
59.
Light of wavelength 589 nm in vacuum passes through a piece of fused quartz of index of refraction n = 1.458. What is the frequency of the light in fused quartz? [Speed of light c = $3.00×10^8 ms^{-1}$ ]
1. A. $5.09×10^{15}$ Hz
2. B. $5.09×10^{14}$ Hz
3. C. $1.77×10^{15}$ Hz
4. D. $1.77×10^{14}$ Hz
Show answer
Answer: B. $5.09×10^{14}$ Hz
AI explanation
Analysis
To solve this problem, we need to understand the relationship between the speed of light, frequency, wavelength, and the refractive index. A key principle in physics is that the frequency of a light wave does not change when it passes from one medium to another; only its speed and wavelength change.
Concept
The fundamental wave equation is:
$c = f \lambda$
Where:
$c$ = speed of light in vacuum ( $3.00 \times 10^8 \text{ m/s}$ )
$f$ = frequency (in Hertz)
$\lambda$ = wavelength (in meters)
Since the frequency ( $f$ ) remains constant regardless of the medium, we can calculate it using the values provided for the vacuum.
Step-by-Step Solution
1. Identify the given values:
Wavelength ( $\lambda$ ) = $589 \text{ nm} = 589 \times 10^{-9} \text{ m}$
Speed of light ( $c$ ) = $3.00 \times 10^8 \text{ m/s}$
Refractive index ( $n$ ) = $1.458$ (Note: This is extra information provided to test if you know that frequency remains constant!)
2. Rearrange the formula to solve for frequency ( $f$ ):
$f = \frac{c}{\lambda}$
3. Substitute the values:
$f = \frac{3.00 \times 10^8}{589 \times 10^{-9}}$
4. Perform the calculation:
$f = \frac{3.00}{589} \times 10^{8 - (-9)}$
$f \approx 0.005093 \times 10^{17}$
To express this in standard scientific notation:
$f \approx 5.09 \times 10^{14} \text{ Hz}$
The refractive index ( $n = 1.458$ ) is irrelevant to the frequency calculation because the frequency is determined by the source of the light, not the medium it travels through.
Conclusion
Comparing our result to the given options, the correct value is $5.09 \times 10^{14} \text{ Hz}$ . This matches option B.
Exam Tip
Always remember the "Frequency Rule": When light travels between different media (like air to glass or water), frequency stays the same, but speed and wavelength change. If a question gives you the refractive index but asks for frequency, don't let it distract you—the frequency is the same as it was in the vacuum!
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60.
Name the type of equilibrium for each position of the ball
1. A.A - unstable, B - neutral, C - stable
2. B.A - stable, B - neutral, C - unstable
3. C.A - stable, B - unstable, C - neutral
4. D.A - unstable, B - stable, C - neutral
Show answer
Answer: D. A - unstable, B - stable, C - neutral
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61.
The near point of a patient's eye is 50.0 cm. What power (in diopters) must a corrective lens have to enable the eye to see clearly an object 25.0 cm away?
1. A.2 diopters
2. B.2.5 diopters
3. C.0.5 diopters
4. D.3 diopters
Show answer
Answer: A. 2 diopters
AI explanation
1. Analyze the Question
The patient is suffering from hypermetropia (long-sightedness). They cannot see objects clearly at the normal near point (25 cm) because their own near point has receded to 50 cm. We need to find the power of a lens that will take an object placed at 25 cm and create a virtual image at the patient's actual near point (50 cm), so the eye can focus on it.
2. Explain the Concept
To solve this, we use the Lens Formula:
$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
Where:
$f$ = focal length of the lens.
$u$ = object distance (where we want to place the object = 25 cm).
$v$ = image distance (where the eye can actually see = -50 cm). • Note: We use a negative sign for $v$ because the image formed by a corrective lens for a long-sighted eye must be virtual and on the same side as the object.
The Power ( $P$ ) of the lens in diopters is given by:
$P = \frac{1}{f (\text{in meters})}$
3. Show the Solution
Step 1: Identify the values
$u = 25\text{ cm} = 0.25\text{ m}$
$v = -50\text{ cm} = -0.50\text{ m}$
Step 2: Calculate the focal length ( $f$ )
$\frac{1}{f} = \frac{1}{0.25} + \frac{1}{-0.50}$
$\frac{1}{f} = 4 - 2$
$\frac{1}{f} = 2\text{ m}^{-1}$
Step 3: Calculate the Power ( $P$ ) Since $P = \frac{1}{f}$ and we already found $\frac{1}{f} = 2$ :
$P = +2.0\text{ diopters}$
4. Identify the Answer
The calculation yields +2.0 diopters. This matches option A.
5. Exam Tip
When dealing with eye defects in physics:
Hypermetropia (Long-sightedness): Always requires a converging (convex) lens, which results in a positive (+) power.
Myopia (Short-sightedness): Always requires a diverging (concave) lens, which results in a negative (-) power.
Always ensure your distance units are in meters before calculating power, or convert your final result carefully!
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62.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.
63.
The electrolyte used in the Nickel-Iron (NiFe) accumulator is
1. A.dilute tetraoxosulphate(VI) acid
2. B.barium chloride solution
3. C.potassium hydroxide solution
4. D.sodium hydroxide solution
Show answer
Answer: C. potassium hydroxide solution
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64.
An open-tube mercury manometer is used to measure the pressure in a gas tank. When the atmospheric pressure is 101,325 $P_a$ , what is the absolute pressure in $P_a$ in the tank if the height of the mercury in the open tube is 25 cm higher. density of mercury = $13600kg/m^3, g = 9.8m/s^2$
1. A.108,986 Pa
2. B.165,238 Pa
3. C.122,364 Pa
4. D.134,645 Pa
Show answer
Answer: D. 134,645 Pa
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65.
The sensitivity of a thermometer is
1. A.All of the above
2. B.how quickly a temperature change can be detected
3. C.the difference between the maximum and the minimum temperature
4. D.the smallest temperature change that can be detected or measured
Show answer
Answer: D. the smallest temperature change that can be detected or measured
AI explanation
1. Analyze the question
The question asks for the definition of "sensitivity" in the context of a thermometer. In physics, sensitivity refers to how responsive an instrument is to small changes in the quantity it is designed to measure.
2. Explain the concept
In measurement science, sensitivity is defined as the ratio of the change in the output (the reading on the thermometer, such as the length of a liquid column) to the change in the input (the temperature).
A highly sensitive thermometer is one that shows a large, noticeable change in its reading for even a very tiny change in temperature. Therefore, the "sensitivity" is essentially determined by the smallest increment of temperature that the device can reliably detect or measure.
Option B describes responsiveness (how fast it reacts), not sensitivity.
Option C describes the range of the thermometer.
3. Show the solution
Sensitivity = $\frac{\text{Change in output}}{\text{Change in input}}$
If a thermometer has high sensitivity, a very small change in temperature (input) will produce a measurable change in the liquid level (output).
Therefore, the limit of this sensitivity is the smallest temperature change that the thermometer can detect. If the temperature changes by an amount smaller than this limit, the thermometer will not show any change, meaning it is not sensitive enough to detect it.
4. Identify the answer
Based on the definition of sensitivity in physical instruments, the correct description is the smallest temperature change that can be detected or measured. This matches Option D.
5. Tip
Think of sensitivity as "precision in detection." If you are using a clinical thermometer, you want it to be very sensitive so that it can detect a tiny fever (e.g., 0.1°C difference). If the thermometer could only measure in whole numbers, it would have low sensitivity!
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2023 JAMB Physics Past Questions and Answers

Questions

1. Analyze the question

2. Explain the concept

3. Show the solution

4. Identify the answer

5. Exam Tip

Analysis

Concept Explanation

Step-by-Step Solution

Identify the Answer

Exam Tip

Analysis

Concept

Step-by-Step Solution

Conclusion

Exam Tip

1. Analyze the question

2. Explain the concept

3. Show the solution

4. Identify the answer

5. Tip

1. Analyze the Question

2. Explain the Concept

3. Show the Solution

4. Identify the Answer

5. Exam Tip

Analysis

Concept Explanation

Step-by-Step Solution

Exam Tip

Analysis

Concept

Step-by-Step Solution

Conclusion

1. Analyze the question

2. Explain the concept

3. Show the solution

4. Identify the answer

5. Exam Tip

1. Analyze the Question

2. Explain the Concept

3. Show the Solution

4. Identify the Answer

5. Exam Tip

Analysis of the Question

Concept Explanation

Step-by-Step Solution

Conclusion

1. Analyze the Question

2. Explain the Concept

3. Show the Solution

4. Identify the Answer

5. Exam Tip

Analysis of the Question

Concept Explanation

Step-by-Step Solution

Conclusion

1. Analyze the Question

2. Explain the Concept

3. Show the Solution

4. Identify the Answer

5. Exam Tip

Analysis

Concept

Solution

Conclusion

Exam Tip

1. Analysis of the Statements

2. Evaluating the Options

3. Conclusion

1. Analyze the Question

2. Explain the Concept

3. Show the Solution

4. Identify the Answer

5. Exam Tip

Analysis

Concept Explanation

Solution

Identification of the Answer