2020 JAMB Physics Past Questions and Answers

Questions

1. 1.

   A transformer has 300 turns of wire in the primary coil and 30 turns in the secondary coil. If the input voltage is 100 volts, the output voltage is

   1. A.5 volts
   2. B.10 volts
   3. C.15 volts
   4. D.20 volts

   Show answer

   Answer: B. 10 volts

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2. 2.

   If in a simple pendulum experiment the length of the inextensible string is increased by a factor of four, its period is increased by a factor of?

   1. A.4
   2. B.$\frac{\pi}{2}$
   3. C.$\frac{1}{4}$
   4. D.2

   Show answer

   Answer: D. 2

   AI explanation

   1. Analyze the question

   We are looking at the relationship between the length ($l$) of a simple pendulum and its period ($T$). We are told the length is increased by a factor of 4, and we need to determine the factor by which the period increases.

   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
   • $l$ = Length of the string
   • $g$ = Acceleration due to gravity

   From this formula, we can see that the period is directly proportional to the square root of the length:

   $T \propto \sqrt{l}$

   3. Show the solution

   Let the initial period be $T_1$ and the initial length be $l_1$.

   $T_1 = k\sqrt{l_1}$$(where$k$ is a constant) Now, the length is increased by a factor of 4, so the new length $l_2 = 4l_1$. Let the new period be $T_2$.$

   $T_2 = k\sqrt{4l_1}$

   Using the laws of indices/surds, we can simplify $\sqrt{4l_1}$ as $\sqrt{4} \times \sqrt{l_1}$:

   $T_2 = k \times 2 \times \sqrt{l_1}$

   $T_2 = 2 \times (k\sqrt{l_1})$

   Since $T_1 = k\sqrt{l_1}$, we substitute it into the equation:

   $T_2 = 2 \times T_1$

   This shows that the new period is 2 times the original period.

   4. Identify the answer

   The period increases by a factor of 2. Comparing this to the given options: A. 4 B. $\frac{\pi}{2}$ C. $\frac{1}{4}$ D. 2

   The correct option is D.

   5. Tip

   Whenever you see a "factor of" question involving a square root (like in pendulums or wave equations), remember: if the variable inside the root increases by $x$, the result increases by $\sqrt{x}$. Here, $\sqrt{4} = 2$. This quick mental check will save you time in the exam hall!

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3. 3.

   One of the following readings represents the measurement of the length of a metal rod using vernier callipers. Taking the reading accuracy into consideration, the most likely one is

   1. A.5.16cm
   2. B.5.165cm
   3. C.5.0cm
   4. D.5.160cm

   Show answer

   Answer: A. 5.16cm

   AI explanation

   Analysis

   To solve this question, we need to understand the precision and least count of a standard vernier calliper.

   Concept: Least Count and Precision

   1. What is a Vernier Calliper? It is a precision instrument used to measure lengths with a higher degree of accuracy than a standard meter rule.
   2. The Least Count: The least count of a standard vernier calliper is typically 0.01 cm (or 0.1 mm). This means the instrument is designed to measure accurately up to two decimal places in centimeters.
   3. Reading Accuracy: When using a vernier calliper, the final digit is often an estimate based on the alignment of the vernier scale with the main scale. Because the instrument's precision is limited to 0.01 cm, any reading provided must reflect this limit.

   Step-by-Step Evaluation

   • Option C (5.0 cm): This is the precision of a standard meter rule. It is too crude for a vernier calliper.
   • Option B (5.165 cm): This measurement has three decimal places. A standard vernier calliper cannot measure to the third decimal place (thousandths of a centimeter); that level of precision would require a micrometer screw gauge.
   • Option D (5.160 cm): While this has two decimal places, the "0" at the end implies a level of precision that is technically redundant for a standard vernier calliper, which reads to the nearest 0.01 cm.
   • Option A (5.16 cm): This reading is expressed to two decimal places (0.01 cm). This perfectly matches the least count and the standard reporting format for a vernier calliper.

   Conclusion

   Since the vernier calliper has a least count of 0.01 cm, the most appropriate reading must be recorded to two decimal places. Option A is the only value that correctly represents the precision capability of the instrument.

   Exam Tip: Always check the number of decimal places in your measurement instruments!

   • Meter rule: 1 decimal place (e.g., 5.1 cm)
   • Vernier calliper: 2 decimal places (e.g., 5.16 cm)
   • Micrometer screw gauge: 3 decimal places (e.g., 5.165 cm)

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4. 4.

   Which of the following instruments consumes the highest current? I. Electric iron II. Television set III. Torchlight IV. Immersion heater 250v 220v 6v 110v 1kW 110W 30W 500W

   1. A.I
   2. B.II
   3. C.III
   4. D.IV

   Show answer

   Answer: C. III

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5. 5.

   Which of the following statements about defects of vision is/are CORRECT?  I. For a long sighted person, close objects appear blurred II. For a short sighted person, distant objects appear blurred  III. Short sight is corrected by using a pair of converging lenses

   1. A.I only
   2. B.II only
   3. C.I and II only
   4. D.II and III only

   Show answer

   Answer: C. I and II only

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6. 6.

   Two divers G and H are at depths 20m and 40m, respectively below the water surface in a lake. The pressure on G is p$_1$ while the pressure on H is P$_2$, If the atmospheric pressure is equivalent to 10m of water, then the value of P$_2$/P$_1$ is?

   1. A.0.50
   2. B.0.60
   3. C.1.67
   4. D.2.00

   Show answer

   Answer: C. 1.67

   AI explanation

   1. Analyze the question

   We are asked to find the ratio of the total pressure at two different depths in a lake. We are given the depths of the divers and the atmospheric pressure expressed in terms of the height of a water column.

   2. Explain the concept

   The total pressure ($P$) at any depth ($h$) in a liquid is given by the sum of the atmospheric pressure ($P_{atm}$) and the hydrostatic pressure exerted by the liquid column ($P_{liquid} = \rho gh$).

   In this problem, the pressure is expressed in terms of the "head" of water (height of water column). Therefore, the formula simplifies to:

   $P = P_{atm} + h$

   Where:

   • $P_{atm} = 10\text{ m}$ (given as the equivalent height of water)
   • $h$ = depth of the diver

   3. Show the solution

   Step 1: Calculate the total pressure on diver G ($P_1$)

   • Depth of G ($h_1$) = $20\text{ m}$
   • $P_1 = P_{atm} + h_1$
   • $P_1 = 10\text{ m} + 20\text{ m} = 30\text{ m}$

   Step 2: Calculate the total pressure on diver H ($P_2$)

   • Depth of H ($h_2$) = $40\text{ m}$
   • $P_2 = P_{atm} + h_2$
   • $P_2 = 10\text{ m} + 40\text{ m} = 50\text{ m}$

   Step 3: Calculate the ratio $P_2 / P_1$

   • Ratio = $P_2 / P_1$
   • Ratio = $50 / 30$
   • Ratio = $5 / 3 \approx 1.666...$

   Rounding to two decimal places, we get 1.67.

   4. Identify the answer

   Comparing our result to the given options, the correct value is 1.67. This matches option C.

   5. Tip

   Always remember that in physics problems involving pressure in liquids, "total pressure" is the sum of the pressure due to the liquid column plus the atmospheric pressure acting on the surface. Never forget to add the atmospheric pressure, or your ratio will be incorrect!

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7. 7.

   The refractive index of a liquid is 1.5. If the velocity of light in vacuum is 3.0 x 10$^8ms^{-1}$, the velocity of light in the liquid is

   1. A.1.5 x 10$^8ms^{-1}$
   2. B.2.0 x 10$^8ms^{-1}$
   3. C.3.0 x 10$^8ms^{-1}$
   4. D.4.5 x 10$^8ms^{-1}$

   Show answer

   Answer: B. 2.0 x 10$^8ms^{-1}$

   AI explanation

   1. Analyze the question

   We are given the refractive index ($n$) of a liquid and the speed of light in a vacuum ($c$). We need to find the speed of light in that specific liquid ($v$).

   2. Explain the concept

   The refractive index of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium. The formula is:

   $n = \frac{c}{v}$

   Where:

   • $n$ = refractive index
   • $c$ = speed of light in vacuum ($3.0 \times 10^8 \, \text{ms}^{-1}$)
   • $v$ = speed of light in the medium (the liquid)

   To find $v$, we rearrange the formula:

   $v = \frac{c}{n}$

   3. Show the solution

   • Given: • $n = 1.5$ • $c = 3.0 \times 10^8 \, \text{ms}^{-1}$

   • Calculation: $$v = \frac{3.0 \times 10^8}{1.5}$$

   To simplify this, you can write $1.5$ as $\frac{3}{2}$:

   $v = \frac{3.0 \times 10^8}{1.5} = \frac{3.0}{1.5} \times 10^8$

   $v = 2.0 \times 10^8 \, \text{ms}^{-1}$

   4. Identify the answer

   Comparing our result to the given options, the correct value is $2.0 \times 10^8 \, \text{ms}^{-1}$, which corresponds to option B.

   5. Tip

   When dealing with refractive index problems, always remember that the speed of light in any medium (other than a vacuum) will always be slower than the speed of light in a vacuum ($3.0 \times 10^8 \, \text{ms}^{-1}$). If your calculated answer is higher than $3.0 \times 10^8$, you have likely multiplied instead of divided!

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8. 8.

   The lower and upper fixed points marked on a Mercury-in-glass thermometer are 210mm apart. The end of the mercury column in the tube is 49mm above the lower fixed point in a room. What is the temperature of the room in degrees Celsius?

   1. A.55.3$^o$C
   2. B.23.3$^o$C
   3. C.49.0$^o$C
   4. D.16.43$^o$C

   Show answer

   Answer: B. 23.3$^o$C

   AI explanation

   Analysis

   To solve this problem, we need to relate the physical length of the mercury column to the temperature scale. In a standard Celsius thermometer, the lower fixed point (ice point) is $0^\circ\text{C}$ and the upper fixed point (steam point) is $100^\circ\text{C}$.

   Concept

   The temperature on a linear scale can be calculated using the ratio of the length of the mercury column above the lower fixed point to the total length between the fixed points:

   $\text{Temperature} = \frac{L_t - L_0}{L_{100} - L_0} \times 100^\circ\text{C}$

   Where:

   • $L_t$ = Length of the mercury column at the room temperature
   • $L_0$ = Length at the lower fixed point ($0^\circ\text{C}$)
   • $L_{100}$ = Length at the upper fixed point ($100^\circ\text{C}$)
   • $(L_{100} - L_0)$ = The total distance between fixed points (given as $210\text{mm}$)
   • $(L_t - L_0)$ = The distance of the mercury column above the lower fixed point (given as $49\text{mm}$)

   Solution

   1. Identify the given values: • Total distance ($L_{100} - L_0$) = $210\text{mm}$ • Distance above lower fixed point ($L_t - L_0$) = $49\text{mm}$

   2. Apply the formula: $$\text{Temperature} = \left( \frac{49}{210} \right) \times 100^\circ\text{C}$$

   3. Perform the calculation: $$\text{Temperature} = \frac{4900}{210}$$ $$\text{Temperature} = \frac{490}{21}$$ $$\text{Temperature} \approx 23.33^\circ\text{C}$$

   Conclusion

   Comparing our result to the given options, $23.3^\circ\text{C}$ matches option B.

   Exam Tip

   When dealing with thermometer problems, always remember that the ratio of the "part" to the "whole" remains constant regardless of the units used (mm, cm, or inches). Just ensure you are consistent with your measurements!

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9. 9.

   Which of the following statements about radioactivity is true? (i) Alpha particle is positively charged (ii) Beta particle is negatively charged (iii) Gamma ray is neutral (iv) Beta particle has the  same mass as helium atom (v) Gamma ray is charged.

   1. A.i, ii, iii, iv only
   2. B.i, ii, iii only
   3. C.iv and v only
   4. D.i, ii and v only

   Show answer

   Answer: B. i, ii, iii only

   AI explanation

   To solve this question, let’s break down the properties of the three main types of radioactive emissions:

   1. Analyze the Statements

   • (i) Alpha particle is positively charged: This is True. An alpha particle consists of 2 protons and 2 neutrons (a helium nucleus), giving it a charge of +2.
   • (ii) Beta particle is negatively charged: This is True. A beta particle is a high-speed electron emitted from the nucleus, which carries a negative charge (-1).
   • (iii) Gamma ray is neutral: This is True. Gamma rays are electromagnetic waves (high-energy photons) and carry no electrical charge.
   • (iv) Beta particle has the same mass as helium atom: This is False. An alpha particle has the same mass as a helium nucleus (4 atomic mass units). A beta particle is an electron, which is extremely light (about 1/1840 the mass of a proton).
   • (v) Gamma ray is charged: This is False. As established in point (iii), gamma rays are neutral electromagnetic radiation.

   2. Evaluate the Options

   Now, let's look at the combinations provided:

   • A: i, ii, iii, iv (Includes the false statement iv)
   • B: i, ii, iii (All these statements are correct)
   • C: iv and v (Both of these statements are false)
   • D: i, ii and v (Includes the false statement v)

   3. Conclusion

   Based on the analysis, statements (i), (ii), and (iii) are the only scientifically accurate descriptions of radioactive emissions. Therefore, the correct combination is i, ii, and iii.

   Exam Tip: When dealing with radioactivity questions, remember the "PEN" rule for particles:

   • Alpha: Heavy, positive (+2), stopped by paper.
   • Beta: Light, negative (-1), stopped by aluminum.
   • Gamma: No mass, neutral, stopped by thick lead.

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10. 10.

    A magnetic needle is suspended first at the earth's north magnetic pole and then at a point on the magnetic equator. The respective angles between the needle and the horizontal are

    1. A.0$^o$ and 0$^o$
    2. B.60$^o$ and 60$^o$
    3. C.90$^o$ and 90$^o$
    4. D.90$^o$ and 0$^o$

    Show answer

    Answer: D. 90$^o$ and 0$^o$

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11. 11.

    In what range of temperature is the expansion of water anomalous?

    1. A.+208$^o$C to +212$^o$C
    2. B.-80$^o$C + -76$^o$C
    3. C.0$^o$C to +4$^o$C
    4. D.-4$^o$C to +0$^o$C

    Show answer

    Answer: C. 0$^o$C to +4$^o$C

    AI explanation

    Analysis of the Question

    The question asks for the specific temperature range where water behaves differently from most other substances regarding its volume and density as it is heated or cooled.

    Concept Explanation: Anomalous Expansion of Water

    Most substances expand when heated and contract when cooled. However, water exhibits a unique behavior known as anomalous expansion.

    1. Normal behavior: As you cool most liquids, they contract (volume decreases) and their density increases.
    2. Water's behavior: When water is cooled from a higher temperature down to $4^\circ\text{C}$, it contracts as expected. However, as it is cooled further from $4^\circ\text{C}$ down to $0^\circ\text{C}$, it begins to expand instead of contracting.
    3. Density implication: Because volume increases as water cools from $4^\circ\text{C}$ to $0^\circ\text{C}$, its density decreases. This is why ice floats on water—it is less dense than liquid water at $4^\circ\text{C}$.

    Step-by-Step Solution

    • Step 1: Identify the temperature at which water reaches its maximum density. This is $4^\circ\text{C}$.
    • Step 2: Observe the behavior between $0^\circ\text{C}$ and $4^\circ\text{C}$. In this range, as temperature increases, the volume of water decreases (it contracts). As temperature decreases, the volume increases (it expands).
    • Step 3: Compare this with the provided options. The range where this "abnormal" or "anomalous" behavior occurs is between $0^\circ\text{C}$ and $4^\circ\text{C}$.

    Conclusion

    Exam Tip

    Remember the "4-degree rule": Water is densest at $4^\circ\text{C}$. Anything below that temperature (down to $0^\circ\text{C}$) causes water to expand, which is why water pipes often burst in very cold climates—the water expands as it turns to ice!

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12. 12.

    In the study of Physics, temperature and heat are often confused with each other. Which of the following statements correctly defines these two elements?

    1. A.Temperature is a measure of the average kinetic energy of the molecules of a substance
    2. B.Heat is a measure of the total kinetic energy of the molecules in a system
    3. C.Different materials require different amounts of heat to cause a given change in temperature
    4. D.All of the above

    Show answer

    Answer: D. All of the above

    AI explanation

    Analysis

    This question tests your fundamental understanding of thermal physics. It requires you to distinguish between the definitions of temperature and heat, and to understand how materials respond to thermal energy.

    Concept Explanation

    1. Temperature: This is a scalar quantity that measures the average kinetic energy of the particles (atoms or molecules) in a substance. It tells us how "hot" or "cold" an object is.
    2. Heat: This is a form of energy in transit. It is the total kinetic energy of all the molecules within a system. Because it is "total" energy, it depends on the mass of the substance, whereas temperature does not.
    3. Specific Heat Capacity: Different substances have different internal structures. Because of this, they require different amounts of heat energy to raise the temperature of a unit mass by one degree Celsius. This property is known as specific heat capacity ($c$).

    Step-by-Step Evaluation

    • Option A: This is the standard scientific definition of temperature. As particles move faster, the average kinetic energy increases, and the temperature rises. This statement is correct.
    • Option B: Heat is indeed the sum total of the kinetic energies of all molecules in a body. This statement is correct.
    • Option C: This describes the principle of specific heat capacity ($Q = mc\Delta\theta$). Since different materials have different values for $c$, they will indeed require different amounts of heat ($Q$) to achieve the same change in temperature ($\Delta\theta$). This statement is correct.

    Since options A, B, and C are all scientifically accurate statements regarding the nature of heat and temperature, the correct choice must encompass all of them.

    Conclusion

    Exam Tip: When you see "All of the above" in a JAMB question, always evaluate every single option carefully. If you can prove that at least two of the options are definitely correct, "All of the above" is almost certainly your answer. Don't rush to pick the first correct option you see!

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13. 13.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

14. 14.

    Natural radioactivity consists of emission?

    1. A.$\alpha$-particles and $\beta$-rays
    2. B.$\alpha$-particles and X-rays
    3. C.$\gamma$-ray and X-rays
    4. D.$\alpha$-particles and $\beta$-rays and $\gamma$-rays

    Show answer

    Answer: D. $\alpha$-particles and $\beta$-rays and $\gamma$-rays

    AI explanation

    Analysis of the Question

    The question asks for the components of natural radioactivity. Natural radioactivity refers to the spontaneous disintegration of unstable atomic nuclei, which results in the emission of ionizing radiation.

    Concept Explanation

    Natural radioactivity involves the emission of three primary types of radiation from the nucleus of an unstable atom:

    1. Alpha ($\alpha$) particles: These are helium nuclei ($^4_2\text{He}$) consisting of two protons and two neutrons. They have a positive charge and are relatively heavy.
    2. Beta ($\beta$) particles: These are high-speed electrons ($^0_{-1}e$) or positrons emitted from the nucleus when a neutron changes into a proton (or vice versa).
    3. Gamma ($\gamma$) rays: These are high-energy electromagnetic waves. Unlike alpha and beta particles, they have no mass and no charge. They are often emitted alongside alpha or beta particles as the nucleus settles into a lower energy state.

    Note on X-rays: X-rays are also electromagnetic waves, but they originate from electron transitions outside the nucleus (in the electron shells), whereas natural radioactivity is a strictly nuclear process. Therefore, X-rays are not considered a product of natural radioactive decay.

    Step-by-Step Solution

    • Step 1: Evaluate the options based on the definition of natural radioactivity.
    • Step 2: Identify that natural radioactivity is defined by the emission of $\alpha$, $\beta$, and $\gamma$ radiations.
    • Step 3: Eliminate options containing X-rays (Options B and C), as X-rays are not products of nuclear decay.
    • Step 4: Compare Option A and Option D. Option A is incomplete because it omits $\gamma$-rays, which are a fundamental component of natural radioactive decay. Option D includes all three standard emissions.

    Conclusion

    The emission associated with natural radioactivity consists of alpha particles, beta particles, and gamma rays. Therefore, Option D is the most comprehensive and accurate answer.

    Exam Tip: Always remember the "Nuclear vs. Orbital" rule: If it comes from the nucleus, it is radioactivity ($\alpha, \beta, \gamma$). If it comes from the electron shells, it is an X-ray. This distinction is a favorite topic for JAMB examiners!

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15. 15.

    The fiqure above represents a block-and-tackle pulley system on which an effort of W Newtons supports a load of 120.0N. If the efficiency of the machine is 40$^o$, then the value of W is

    1. A.28.0N
    2. B.48.0N
    3. C.288.0N
    4. D.50.0N

    Show answer

    Answer: A. 28.0N

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16. 16.

    Tha mass of a proton is approximately equal to that of

    1. A.an $\alpha$-particle
    2. B.a $\beta$-Particle
    3. C.a neutron
    4. D.an electron

    Show answer

    Answer: C. a neutron

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17. 17.

    A ship travelling towards a cliff receives the echo of its whistle after 3.5 seconds. A short while later, it receives the echo after 2.5 seconds. If the speed of sound in air under the prevalling condition is 250ms -1, how much closer is the ship to the cliff?

    1. A.10m
    2. B.350m
    3. C.175m
    4. D.125m

    Show answer

    Answer: D. 125m

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18. 18.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

19. 19.

    In an experiment in which molten naphthalene is allowed to cool, the cooling curve i n the figure was obtained. The temperature 80$^o$C is known as the

    1. A.cooling temperature
    2. B.boiling point
    3. C.melting point
    4. D.vaporization point

    Show answer

    Answer: D. vaporization point

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20. 20.

    A machine gun with a mass of 5kg fires a 50g bullet at a speed of 100 ms$^{-1}$. The recoil speed of the machine gun is

    1. A.0.5 ms$^{-1}$
    2. B.1.5 ms$^{-1}$
    3. C.1 ms$^{-1}$
    4. D.2ms$^-1$

    Show answer

    Answer: C. 1 ms$^{-1}$

    AI explanation

    Analysis

    To solve this problem, we apply the Law of Conservation of Linear Momentum. This law states that in a closed system, the total momentum before an event (firing the gun) is equal to the total momentum after the event.

    Concept

    The formula for the conservation of momentum is:

    $m_g v_g + m_b v_b = 0$

    Where:

    • $m_g$ = mass of the gun
    • $v_g$ = recoil velocity of the gun
    • $m_b$ = mass of the bullet
    • $v_b$ = velocity of the bullet

    Since the gun and bullet are initially at rest, the total initial momentum is zero. When fired, the bullet moves in one direction (positive) and the gun recoils in the opposite direction (negative).

    Step-by-Step Solution

    1. Identify the given values:

    • Mass of the gun ($m_g$) = $5\text{ kg}$
    • Mass of the bullet ($m_b$) = $50\text{ g} = 0.05\text{ kg}$ (Always convert grams to kilograms!)
    • Velocity of the bullet ($v_b$) = $100\text{ ms}^{-1}$
    • Recoil velocity of the gun ($v_g$) = ?

    2. Set up the equation:

    $m_g v_g = -m_b v_b$

    (The negative sign indicates the opposite direction of the recoil)

    3. Substitute the values:

    $5 \times v_g = -(0.05 \times 100)$

    $5 \times v_g = -5$

    4. Solve for $v_g$:

    $v_g = \frac{-5}{5}$

    $v_g = -1\text{ ms}^{-1}$

    The magnitude of the recoil speed is $1\text{ ms}^{-1}$.

    Conclusion

    Comparing our result with the provided options, the correct answer is C.

    Exam Tip

    Always check your units before calculating! A common mistake in JAMB Physics is forgetting to convert grams (g) to kilograms (kg). If you had used 50 instead of 0.05, you would have gotten an answer of 1000, which would lead you to choose the wrong option. Always ensure mass is in kg and velocity is in ms⁻¹.

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21. 21.

    Which of the following statements on the use of X-rays is incorrect? X-rays are used

    1. A.In a hospital to obtain photographs of tissues and bones in the body
    2. B.For the treatment of malignant growths like cancer cells
    3. C.In detecting fingerprints
    4. D.To reveal hidden flaws in metal castings and welded joints work of art

    Show answer

    Answer: C. In detecting fingerprints

    AI explanation

    Analysis of the Question

    This question tests your knowledge of the practical applications of X-rays in medicine, industry, and security. We need to identify which of the listed options is not a valid use of X-rays.

    Concept Explanation

    X-rays are high-energy electromagnetic radiations with short wavelengths. Their properties include:

    • High Penetrating Power: They can pass through soft tissues but are absorbed by denser materials like bones or metals.
    • Ionizing Radiation: They can damage or destroy living cells, which is why they are used in radiotherapy.
    • Fluorescence: They cause certain materials to glow.

    Let's evaluate the options:

    • Option A: X-rays are widely used in radiography to visualize bones and dense tissues because bones absorb more X-rays than soft tissue, creating a contrast on the film. This is correct.
    • Option B: Because X-rays are ionizing, they can be used in controlled doses to kill cancerous cells (radiotherapy). This is correct.
    • Option C: Fingerprint detection is typically done using optical scanners, powders, or chemical reagents (like ninhydrin) that react with the amino acids in sweat. X-rays are not used for this purpose. This is incorrect.
    • Option D: In industrial radiography, X-rays are used to inspect metal castings and welds for internal cracks or air bubbles, as these flaws show up as variations in density. This is correct.

    Step-by-Step Solution

    1. Review the properties: X-rays are used for imaging (A), medical treatment (B), and industrial inspection (D).
    2. Evaluate the outlier: Fingerprint detection relies on surface patterns and chemical residues, not the high-penetration imaging capabilities of X-rays.
    3. Conclusion: Since the question asks for the incorrect statement, Option C is the right choice.

    Exam Tip

    When you see "Which of the following is incorrect/not true," always look for the option that describes a process involving a different part of the electromagnetic spectrum. For example, fingerprints are usually detected using visible light or chemical forensic methods, not ionizing radiation like X-rays.

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22. 22.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

23. 23.

    Heat is supplied uniformly at the rate of 100W to 1.0 x 10$^{-2}$kg of a liquid for 20 seconds. If the temperature of the liquid rises by 5$^o$C, then the specific heat capacity of the liquid is

    1. A.2.0 x 10$^2$Jkg$^-1$K$^-1$
    2. B.2.0 x 10$^2$Jkg$^-1$
    3. C.4.0 x 10$^4$Jkg$^-1$K$^-1$
    4. D.4.0 x 10$^4$Jkg$^-1$

    Show answer

    Answer: C. 4.0 x 10$^4$Jkg$^-1$K$^-1$

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24. 24.

    A convex mirror is used as a driving mirror because  I. its image is erect      II. It has a large field of view III. It has a long focal length  Identify the CORRECT statement(s)

    1. A.I and III only
    2. B.I and II only
    3. C.II and IIII only
    4. D.I, II and III only

    Show answer

    Answer: B. I and II only

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25. 25.

    If a source of solid is moving, a stationary listener will hear a sound of different frequency. This is called?

    1. A.doppler effect
    2. B.resonance
    3. C.ultra sound
    4. D.rarefaction

    Show answer

    Answer: A. doppler effect

    AI explanation

    1. Analyze the Question

    The question describes a physical phenomenon where the frequency of a sound wave perceived by a listener changes because the source of the sound is in motion relative to the listener. You are asked to identify the name of this specific effect.

    2. Explain the Concept

    This phenomenon is known as the Doppler Effect.

    • How it works: When a source of sound moves towards a stationary listener, the sound waves are "compressed," leading to a shorter wavelength and a higher frequency (a higher pitch). Conversely, when the source moves away, the waves are "stretched," leading to a longer wavelength and a lower frequency (a lower pitch).
    • Real-life example: Think of an ambulance siren. As it approaches you, the pitch sounds higher; as it passes you and moves away, the pitch drops significantly.

    3. Evaluate the Options

    • A. Doppler effect: This is the correct term for the change in frequency due to relative motion between a source and an observer.
    • B. Resonance: This occurs when an object is forced to vibrate at its natural frequency by an external source, leading to an increase in amplitude.
    • C. Ultrasound: This refers to sound waves with frequencies higher than the upper audible limit of human hearing (above 20,000 Hz).
    • D. Rarefaction: This is a region in a longitudinal wave where the particles are furthest apart (the opposite of compression).

    4. Conclusion

    Based on the definition provided in the question, the phenomenon described is the Doppler effect.

    Exam Tip: Whenever you see a question involving a "moving source" or "moving observer" and a change in "frequency" or "pitch," immediately think of the Doppler Effect. It is a very common topic in JAMB Physics!

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26. 26.

    When a sound wave passes from air into water its

    1. A.speed and frequency increases but its wavelength remains the same
    2. B.speed and wavelength increases but its frequency remains the same
    3. C.speed decreases
    4. D.speed increases but its frequency and wavelength decreases

    Show answer

    Answer: B. speed and wavelength increases but its frequency remains the same

    AI explanation

    Analysis

    This question tests your understanding of wave properties as they travel through different media. To solve this, we must look at how the physical properties of a wave (speed, frequency, and wavelength) behave when moving from a less dense medium (air) to a denser medium (water).

    Concept Explanation

    The relationship between the speed ($v$), frequency ($f$), and wavelength ($\lambda$) of a wave is given by the formula:

    $v = f \times \lambda$

    1. Frequency ($f$): This is determined entirely by the source of the sound. When a wave moves from one medium to another, the frequency remains constant.
    2. Speed ($v$): Sound travels faster in denser media because the particles are closer together, allowing the vibration to be transmitted more efficiently. Therefore, sound travels faster in water than in air.
    3. Wavelength ($\lambda$): Since $v = f \times \lambda$ and $f$ is constant, if the speed ($v$) increases, the wavelength ($\lambda$) must also increase to maintain the equality.

    Step-by-Step Solution

    1. Identify the constant: As the sound wave enters the water, its frequency ($f$) does not change.
    2. Determine the speed change: Sound travels significantly faster in water (approx. 1,480 m/s) than in air (approx. 340 m/s). Thus, the speed ($v$) increases.
    3. Determine the wavelength change: Using the formula $\lambda = v / f$, since $v$ increases and $f$ is constant, $\lambda$ must increase.
    4. Conclusion: Both speed and wavelength increase, while frequency remains the same.

    Identifying the Answer

    Comparing our conclusion to the options provided:

    • A is incorrect because frequency does not change.
    • B is correct because it states that speed and wavelength increase while frequency remains constant.
    • C is incorrect because speed actually increases.
    • D is incorrect because wavelength does not decrease.

    Exam Tip: Always remember the "Source Rule": The frequency of a wave is a "DNA" trait—it is fixed by the source and never changes regardless of the medium. If you know the frequency is constant, you can immediately eliminate any option that suggests it changes!

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27. 27.

    A hydrometer is an instrument for measuring the

    1. A.a depth of water of water in a vessel
    2. B.relative density of a liquid by the method of flotation
    3. C.relative density of a liquid by finding the apparent loss in weight
    4. D.relative humidity of the air

    Show answer

    Answer: B. relative density of a liquid by the method of flotation

    AI explanation

    Analysis of the Question

    The question asks for the specific function of a hydrometer. To answer this, we need to understand the principle of flotation and how it relates to the density of liquids.

    Concept Explanation

    A hydrometer is a glass instrument used to measure the relative density (or specific gravity) of liquids.

    1. Principle of Flotation: The hydrometer works based on Archimedes' principle. When placed in a liquid, it sinks until the weight of the liquid it displaces is equal to its own weight.
    2. How it works: • In a denser liquid, the hydrometer will float higher because it needs to displace less volume of the liquid to equal its own weight. • In a less dense liquid, the hydrometer will sink deeper.
    3. Calibration: The stem of the hydrometer is graduated with a scale. By observing the level at which the liquid surface touches the stem, you can directly read the relative density of the liquid.

    Step-by-Step Evaluation of Options

    • A (Depth of water): This is incorrect. Instruments like a sounding line or a pressure gauge are used for depth.
    • B (Relative density by flotation): This is correct. As explained above, the hydrometer relies on the principle of flotation to determine how dense a liquid is relative to water.
    • C (Relative density by apparent loss in weight): This is incorrect. This method describes the use of a density bottle or a Nicholson’s hydrometer (which is different from the standard glass hydrometer) using a balance to measure weight loss.
    • D (Relative humidity): This is incorrect. Relative humidity is measured using a hygrometer.

    Conclusion

    The hydrometer is specifically designed to measure the relative density of liquids by observing how high or low it floats in the liquid.

    Exam Tip: Always distinguish between a hydrometer (for liquid density) and a hygrometer (for atmospheric humidity). They sound similar, but they measure completely different physical properties!

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28. 28.

    A solid weighs 4.8g in air, 2.8g in water and 3.2g in Kerosine. The ratio of density of the solid to that of the kerosine is

    1. A.2
    2. B.$\frac{3}{2}$
    3. C.$\frac{2}{3}$
    4. D.3

    Show answer

    Answer: D. 3

    AI explanation

    1. Analyze the Question

    We are given the weight of a solid in three different media: air, water, and kerosene. We need to find the ratio of the density of the solid to the density of kerosene.

    Given:

    • Weight of solid in air ($W_a$) = 4.8 g
    • Weight of solid in water ($W_w$) = 2.8 g
    • Weight of solid in kerosene ($W_k$) = 3.2 g

    2. Explain the Concept

    The density of a substance relative to a liquid can be determined using the principle of upthrust (Archimedes' Principle).

    • Upthrust in a liquid = Weight in air - Weight in liquid.
    • Relative Density (RD) of a solid = $\frac{\text{Weight in air}}{\text{Loss of weight in water}}$ (if comparing to water).
    • More generally, the ratio of the density of a solid ($\rho_s$) to the density of a liquid ($\rho_l$) is given by: $$\frac{\rho_s}{\rho_l} = \frac{\text{Weight of solid in air}}{\text{Loss of weight in liquid}}$$ Where the "Loss of weight in liquid" is the upthrust provided by that specific liquid.

    3. Show the Solution

    Step 1: Calculate the loss of weight of the solid in kerosene. The loss of weight in kerosene is the difference between the weight in air and the weight in kerosene:

    $\text{Loss in kerosene} = W_a - W_k$

    $\text{Loss in kerosene} = 4.8\text{g} - 3.2\text{g} = 1.6\text{g}$

    Step 2: Use the density ratio formula. The ratio of the density of the solid ($\rho_s$) to the density of kerosene ($\rho_k$) is the ratio of the weight of the solid in air to the upthrust (loss of weight) in kerosene:

    $\frac{\rho_s}{\rho_k} = \frac{W_a}{W_a - W_k}$

    $\frac{\rho_s}{\rho_k} = \frac{4.8}{1.6}$

    Step 3: Simplify the fraction.

    $\frac{4.8}{1.6} = \frac{48}{16} = 3$

    4. Identify the Answer

    The calculation gives us 3. Comparing this to the provided options: A. 2 B. 3/2 C. 2/3 D. 3

    The correct option is D.

    5. Tip

    When solving "weight in liquid" problems, always remember that the loss of weight is equal to the weight of the liquid displaced. If you are asked for the density of the liquid itself, you can use the ratio of the loss of weight in that liquid to the loss of weight in water!

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29. 29.

    What is the cost of running five 50W lamps and four 100W lamps for 10 hours if electrical energy costs 2 Kobo per KWh?

    1. A.N0.65
    2. B.N0.39
    3. C.N3.90
    4. D.N0.13

    Show answer

    Answer: D. N0.13

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30. 30.

    Which of the following can be described as high tension transmission?

    1. A.High resistance and low voltage
    2. B.Low current and high voltage
    3. C.High current and low voltage
    4. D.High current and low resistance

    Show answer

    Answer: B. Low current and high voltage

    AI explanation

    Analysis

    The question asks for the characteristics of "high tension" (HT) transmission lines, which are the large power lines you see on tall metal pylons across the country. To understand this, we must look at how electrical power is transmitted from power stations to our homes.

    Concept: Power Transmission

    Electrical power ($P$) is transmitted using the formula:

    $P = IV$

    Where:

    • $P$ is the power (measured in Watts)
    • $I$ is the current (measured in Amperes)
    • $V$ is the voltage (measured in Volts)

    Power stations generate a fixed amount of power. To minimize energy loss due to heat (which occurs in the wires according to the formula $H = I^2Rt$), power companies want to keep the current ($I$) as low as possible.

    Since $P = IV$, if we want to keep $P$ constant while making $I$ very small, we must make $V$ (the voltage) very large. This is why it is called "High Tension" or "High Voltage" transmission.

    Step-by-Step Solution

    1. Identify the goal: The goal of long-distance power transmission is to reduce energy loss in the cables.
    2. Analyze the heat loss: Energy loss in cables is given by $P_{loss} = I^2R$. To minimize this, $I$ must be kept as low as possible.
    3. Apply the power formula: Since $P = IV$, to transmit the same amount of power ($P$) with a very low current ($I$), the voltage ($V$) must be stepped up to a very high value.
    4. Conclusion: High tension transmission is characterized by high voltage to allow for low current, which prevents the wires from overheating and losing energy.

    Correct Option

    Comparing this to your options:

    • A is incorrect because high resistance would cause massive energy loss.
    • B is correct because it describes the high voltage and low current required for efficient transmission.
    • C is incorrect because high current would cause the wires to melt or lose too much energy.
    • D is incorrect because high current is the opposite of what is needed for high tension.

    Exam Tip: Always remember the phrase "Step-up to save." Transformers "step up" the voltage to a high level so that the current is "stepped down" to a low level, saving energy during transmission.

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31. 31.

    The linear expansivity of brass is 2 x 10$^{-5}$  $^oC^{-1}$. If the volume of piece of brass is 10cm$^3$ at 0$^o$C. What will be its volume at 100$^o$C?

    1. A.10.06cm$^3$
    2. B.10.04 cm$^3$
    3. C.10.02 cm$^3$
    4. D.10.20 cm$^3$

    Show answer

    Answer: A. 10.06cm$^3$

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32. 32.

    Which of the following pairs is part of the electromagnetic spectrum?  I. Radio waves II. sound waves III. Gamma rays IV. water waves

    1. A.I and II
    2. B.III and IV
    3. C.I and III
    4. D.II and IV

    Show answer

    Answer: C. I and III

    AI explanation

    Analysis

    To solve this question, we need to identify which of the listed waves belong to the electromagnetic (EM) spectrum. The electromagnetic spectrum consists of waves that do not require a material medium for propagation and travel at the speed of light ($3 \times 10^8 \text{ m/s}$) in a vacuum.

    Concept Explanation

    The electromagnetic spectrum includes the following, in order of increasing frequency:

    1. Radio waves
    2. Microwaves
    3. Infrared radiation
    4. Visible light
    5. Ultraviolet radiation
    6. X-rays
    7. Gamma rays

    Why the others are excluded:

    • Sound waves: These are mechanical waves. They require a material medium (solid, liquid, or gas) to travel and cannot propagate through a vacuum.
    • Water waves: These are also mechanical waves that require a medium (water) to propagate.

    Step-by-Step Solution

    1. Evaluate I (Radio waves): Radio waves are part of the electromagnetic spectrum. (Correct)
    2. Evaluate II (Sound waves): Sound waves are mechanical, longitudinal waves, not electromagnetic. (Incorrect)
    3. Evaluate III (Gamma rays): Gamma rays are high-frequency electromagnetic waves. (Correct)
    4. Evaluate IV (Water waves): Water waves are mechanical surface waves. (Incorrect)

    Comparing our findings with the options:

    • I and III are the correct components. This corresponds to option C.

    Exam Tip

    Remember the mnemonic "Raging Martians Invaded Venus Using X-ray Guns" to recall the order of the electromagnetic spectrum:

    • Radio waves
    • Microwaves
    • Infrared
    • Visible light
    • Ultraviolet
    • X-rays
    • Gamma rays

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33. 33.

    In which of the following diagrams is the length of the tube equal to one wavelength?

    1. A.a
    2. B.b
    3. C.c
    4. D.d

    Show answer

    Answer: A. a

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34. 34.

    A substance has half of 3 min. After 6 min, the count rate was observed to be 400. What was its count rate at zero time?

    1. A.1600
    2. B.1200
    3. C.200
    4. D.2400

    Show answer

    Answer: A. 1600

    AI explanation

    1. Analyze the Question

    We are dealing with a radioactive decay problem. We know the half-life ($T_{1/2}$) is 3 minutes, the elapsed time ($t$) is 6 minutes, and the final count rate ($N_t$) is 400. We need to find the initial count rate ($N_0$).

    2. Explain the Concept

    The radioactive decay formula relates the initial amount to the final amount over a period of time:

    $N_t = N_0 \left( \frac{1}{2} \right)^n$

    Where:

    • $N_t$ = Final count rate
    • $N_0$ = Initial count rate
    • $n$ = Number of half-lives elapsed, calculated as $n = \frac{t}{T_{1/2}}$

    3. Show the Solution

    Step 1: Calculate the number of half-lives ($n$)

    $n = \frac{\text{Total time}}{\text{Half-life}} = \frac{6 \text{ min}}{3 \text{ min}} = 2$

    This means the substance has gone through 2 half-lives.

    Step 2: Use the decay formula

    $400 = N_0 \left( \frac{1}{2} \right)^2$

    $400 = N_0 \left( \frac{1}{4} \right)$

    Step 3: Solve for $N_0$ Multiply both sides by 4:

    $N_0 = 400 \times 4$

    $N_0 = 1600$

    4. Identify the Answer

    The initial count rate was 1600. This corresponds to option A.

    5. Exam Tip

    For simple half-life problems where the number of half-lives is a whole number, you don't always need the formula. Just work backward:

    • At 6 mins: 400
    • At 3 mins (one half-life earlier): $400 \times 2 = 800$
    • At 0 mins (two half-lives earlier): $800 \times 2 = 1600$ This "doubling back" method is faster and helps you avoid calculation errors during the exam!

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35. 35.

    A few grains of table salt were put in a cup of cold water, kept at constant temperature and left undistributed. Eventually all the water tested salty. This action is due to?

    1. A.convection
    2. B.osmosis
    3. C.capillarity
    4. D.diffusion

    Show answer

    Answer: D. diffusion

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36. 36.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

37. 37.

    The force required to make an object of mass m, travelling with velocity v, turn in a circle of radius r is

    1. A.$\frac{mv^2}{r}$
    2. B.$\frac{mr^2}{x}$
    3. C.$\frac{mr}{v}$
    4. D.$\frac{mv}{r^2}$

    Show answer

    Answer: A. $\frac{mv^2}{r}$

    AI explanation

    Analysis

    The question asks for the force required to keep an object of mass $m$ moving in a circular path of radius $r$ with a constant velocity $v$. This is a fundamental concept in circular motion known as centripetal force.

    Concept

    When an object moves in a circular path, it is constantly changing its direction. Even if the speed ($v$) remains constant, the change in direction means the object is accelerating. This acceleration is directed toward the center of the circle and is called centripetal acceleration ($a_c$).

    The formula for centripetal acceleration is:

    $a_c = \frac{v^2}{r}$

    According to Newton's Second Law of Motion ($F = ma$), the force required to produce this acceleration is the product of the mass and the centripetal acceleration.

    Solution

    1. Identify the variables: • Mass = $m$ • Velocity = $v$ • Radius = $r$
    2. Apply Newton's Second Law: • $F = m \times a_c$
    3. Substitute the centripetal acceleration formula: • $F = m \times \left(\frac{v^2}{r}\right)$
    4. Simplify: • $F = \frac{mv^2}{r}$

    This force is what we call the centripetal force. It is the "center-seeking" force that prevents the object from flying off in a straight line (tangent to the circle).

    Conclusion

    Comparing our result to the given options, the correct expression is $\frac{mv^2}{r}$.

    Exam Tip: Always remember that "centripetal" means "center-seeking." If you ever forget the formula, remember that the force must increase if the speed increases (square of velocity) and must decrease if the radius of the turn increases (inversely proportional to $r$). This logic helps you eliminate options like C and D quickly!

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38. 38.

    Which of the following conditions are necessary and sufficient for total internal reflection to take place at the boundary between two optical media? I. Light is passing from optical denser medium to optically less dense medium II. Light is passing from optically less dense medium to optically denser medium III. Angle of incidence is greater than a certain critical value IV. Angle of incidence is lesser  than a certain critical value

    1. A.I and II only
    2. B.II only III only
    3. C.III and IV only
    4. D.I and III only

    Show answer

    Answer: D. I and III only

    AI explanation

    Analysis of the Question

    Total internal reflection (TIR) is a phenomenon in optics that occurs when light traveling through a medium hits a boundary with a less dense medium at a specific angle. To identify the correct conditions, we must look at the physical requirements for this phenomenon to occur.

    Concept Explanation

    Total internal reflection occurs only when two specific conditions are met:

    1. Direction of Light: Light must travel from a medium with a higher refractive index (optically denser) to a medium with a lower refractive index (optically less dense). If light travels from a less dense to a denser medium, it bends towards the normal, making it impossible for the light to be reflected back into the first medium.
    2. Angle of Incidence: The angle of incidence must be greater than the critical angle ($c$). The critical angle is the angle of incidence for which the angle of refraction is exactly $90^\circ$. If the angle of incidence is less than the critical angle, the light will refract (pass through) into the second medium.

    Step-by-Step Solution

    • Condition I: "Light is passing from optically denser medium to optically less dense medium." This is a necessary condition for TIR.
    • Condition II: "Light is passing from optically less dense medium to optically denser medium." This is incorrect because light would bend towards the normal, not reflect.
    • Condition III: "Angle of incidence is greater than a certain critical value." This is a sufficient condition. Once the light is in the denser medium, exceeding the critical angle ensures the light reflects back.
    • Condition IV: "Angle of incidence is lesser than a certain critical value." This is incorrect because, at angles less than the critical angle, refraction occurs instead of total internal reflection.

    Comparing these to the options provided, conditions I and III are the correct requirements.

    Conclusion

    Exam Tip

    Remember the acronym "D-G" for Total Internal Reflection:

    • Denser to rarer medium.
    • Greater than the critical angle. If you remember "D-G," you will never miss a question on the conditions for TIR!

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