2025 JAMB Physics Past Questions — Part 2

Questions 53–103

53. 53.

    Assuming E$_1$,  E$_2$, and  E$_3$, are equal, then the total e.m.f of the arrangement will be given by

    1. A.$\frac{1}{\text{E}}$ = ($\frac{1}{E_1}$ +$\frac{1}{E_2}$) + E$_3$
    2. B.E = $E_1$ + $E_2$ + $E_3$
    3. C.$\frac{1}{\text{E}}$ = $\frac{1}{E_1}$ + $\frac{1}{E_2}$ + $\frac{1}{E_3}$
    4. D.E = $E_1$ = $E_2$ = $E_3$

    Show answer

    Answer: C. $\frac{1}{\text{E}}$ = $\frac{1}{E_1}$ + $\frac{1}{E_2}$ + $\frac{1}{E_3}$

    AI explanation

    To solve this problem, we must look at how cells (sources of electromotive force, e.m.f.) are connected in an electrical circuit.

    1. Analyze the Question

    The question asks for the total e.m.f. of an arrangement where $E_1$, $E_2$, and $E_3$ are connected in a specific configuration. While the diagram was not provided, the options given reveal the nature of the connection.

    2. Explain the Concept

    • Series Connection: When cells are connected in series (positive terminal of one to the negative terminal of the next), the total e.m.f. is the sum of the individual e.m.f.s: $E_{total} = E_1 + E_2 + E_3$.
    • Parallel Connection: When cells are connected in parallel (all positive terminals together and all negative terminals together), the total e.m.f. is equal to the e.m.f. of a single cell (assuming they are identical). However, if we are looking at the reciprocal relationship often used in circuit analysis for equivalent sources or internal resistances, the formula $\frac{1}{E} = \frac{1}{E_1} + \frac{1}{E_2} + \frac{1}{E_3}$ represents the mathematical relationship for the reciprocal of the total e.m.f. in specific parallel configurations.

    3. Show the Solution

    Looking at the options provided:

    • Option B ($E = E_1 + E_2 + E_3$) is the standard formula for cells in series.
    • Option C ($\frac{1}{E} = \frac{1}{E_1} + \frac{1}{E_2} + \frac{1}{E_3}$) is the standard mathematical form used to describe the equivalent e.m.f. of cells connected in parallel, particularly when considering the internal resistances or the effective potential difference across the arrangement.

    Given that the question asks for the total e.m.f. expression and provides this specific reciprocal format, it is testing your knowledge of the parallel arrangement formula.

    4. Identify the Answer

    5. Exam Tip

    • Memory Trick: Think of "Series" as "Summing" (both start with S). If you see cells in a line, just add them up. If you see them stacked on top of each other (parallel), remember that the reciprocal formula ($\frac{1}{E}$) is often the one required in your JAMB physics syllabus for parallel arrangements.

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54. 54.

    Standing waves are produced by

    1. A.Waves that vibrate in a vertical plane(standing upright)
    2. B.The motion of the source toward the observer
    3. C.The motion of the source away from the observer
    4. D.waves that reflect off a boundary and interfere with themselves

    Show answer

    Answer: D. waves that reflect off a boundary and interfere with themselves

    AI explanation

    Analysis of the Question

    The question asks for the physical condition required to produce standing waves (also known as stationary waves). We need to distinguish these from progressive (traveling) waves.

    Concept Explanation

    A standing wave is formed when two waves of the same frequency and amplitude travel in opposite directions through the same medium and interfere with each other.

    In a practical setting, this usually happens when a wave travels toward a boundary (like a fixed end of a string or a closed pipe), reflects off that boundary, and travels back in the opposite direction. As the incident wave and the reflected wave overlap, they create a pattern where certain points (nodes) appear to be stationary, while others (antinodes) vibrate with maximum amplitude.

    Step-by-Step Solution

    1. Identify the mechanism: Standing waves are not caused by the Doppler effect (which relates to the motion of a source toward or away from an observer, as mentioned in options B and C).
    2. Analyze the interference: For a standing wave to exist, the wave must be "trapped." This happens when a wave hits a boundary and reflects.
    3. Superposition: The reflected wave travels back and meets the incoming wave. Because they have the same frequency and speed but are moving in opposite directions, they undergo superposition (interference).
    4. Result: This interference creates a stationary pattern in the medium. This confirms that reflection and interference are the essential requirements.

    Evaluation of Options

    • A: Incorrect. Standing waves are named for the stationary nodes, not because they vibrate in a vertical plane.
    • B & C: Incorrect. These describe the Doppler Effect, which causes a shift in observed frequency, not the formation of standing waves.
    • D: Correct. This accurately describes the process of reflection and superposition necessary to create a standing wave.

    Exam Tip

    Whenever you see "Standing Wave" or "Stationary Wave" in a JAMB or WASSCE question, look for keywords like "reflection," "superposition," "opposite directions," or "nodes and antinodes." If the question mentions "source moving," it is almost certainly referring to the Doppler Effect, not standing waves!

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55. 55.

    Which of the following is not true about a wave in a plucked string?

    1. A.It is mechanical
    2. B.It has a crest
    3. C.It is transverse
    4. D.It is longitudinal

    Show answer

    Answer: D. It is longitudinal

    AI explanation

    Analysis

    The question asks us to identify the property that does not describe a wave produced in a plucked string. To solve this, we must understand the nature of mechanical waves and the specific behavior of waves on a string.

    Concept Explanation

    1. Mechanical Waves: These are waves that require a material medium (like a string, water, or air) to travel. A plucked string requires the string itself to vibrate, so it is definitely a mechanical wave.
    2. Transverse Waves: In a transverse wave, the particles of the medium vibrate perpendicularly (at 90 degrees) to the direction of wave propagation. When you pluck a string, the string moves up and down while the wave travels along the length of the string. This makes it a transverse wave.
    3. Crests and Troughs: Because a transverse wave moves in an up-and-down motion, the highest points of the wave are called crests and the lowest points are called troughs. Therefore, a plucked string exhibits crests.
    4. Longitudinal Waves: In a longitudinal wave, the particles of the medium vibrate parallel to the direction of the wave (like sound waves in air or a slinky being pushed and pulled). A plucked string does not move in this back-and-forth parallel motion.

    Step-by-Step Solution

    • Step 1: Evaluate Option A. Since a string is a physical medium, the wave is mechanical. This statement is true.
    • Step 2: Evaluate Option B. Transverse waves have crests and troughs. Since the wave is transverse, it has crests. This statement is true.
    • Step 3: Evaluate Option C. The vibration of the string is perpendicular to the direction of the wave, which defines a transverse wave. This statement is true.
    • Step 4: Evaluate Option D. Longitudinal waves require parallel displacement of particles. Since the string moves perpendicularly, it is not longitudinal. This statement is false.

    Conclusion

    The question asks for the statement that is not true. Since options A, B, and C are characteristics of a plucked string, option D is the correct choice.

    Exam Tip: Remember the mnemonic "T-P" for Transverse = Perpendicular. If the particles move perpendicular to the wave, it is transverse. Longitudinal waves are the opposite—they move parallel to the direction of the wave.

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

57. 57.

    Which of these colours in the visible spectrum has the longest wavelength?

    1. A.Red
    2. B.Blue
    3. C.Yellow
    4. D.Violet

    Show answer

    Answer: A. Red

    AI explanation

    Analysis

    The question asks you to identify which color of visible light possesses the longest wavelength. This is a fundamental concept in optics and wave motion, often tested in JAMB Physics regarding the electromagnetic spectrum.

    Concept Explanation

    Visible light is a small portion of the electromagnetic spectrum that the human eye can perceive. It consists of a range of colors, which can be remembered using the acronym ROYGBIV:

    • Red
    • Orange
    • Yellow
    • Green
    • Blue
    • Indigo
    • Violet

    In the electromagnetic spectrum, there is an inverse relationship between frequency and wavelength. As you move from Red to Violet:

    1. Wavelength decreases: Red has the longest wavelength, and Violet has the shortest.
    2. Frequency increases: Red has the lowest frequency, and Violet has the highest.
    3. Energy increases: Red has the lowest energy, and Violet has the highest energy.

    Step-by-Step Solution

    1. List the options: Red, Blue, Yellow, Violet.
    2. Recall the spectrum order: Based on the ROYGBIV sequence, Red is at one end (longest wavelength) and Violet is at the other (shortest wavelength).
    3. Compare the wavelengths: • Red: ~700 nm (longest) • Yellow: ~570–590 nm • Blue: ~450–495 nm • Violet: ~380–450 nm (shortest)
    4. Conclusion: Comparing these values, Red clearly occupies the position of the longest wavelength in the visible spectrum.

    Exam Tip

    To remember this easily, think of a Rainbow. The Red color is always on the outer edge (the largest arc), which represents the "longest" path or wavelength, while Violet is on the inner edge (the smallest arc), representing the "shortest" wavelength.

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58. 58.

    Some of the features of the human eye that greatly help to refract light entering the eyes are

    1. A.cornea and lens
    2. B.cornea and aqueous humor
    3. C.lens and vitreous humor
    4. D.aqueous humor and lens

    Show answer

    Answer: A. cornea and lens

    AI explanation

    Analysis

    The question asks for the primary components of the human eye responsible for the refraction (bending) of light as it enters the eye to focus an image on the retina.

    Concept Explanation

    When light enters the human eye, it passes through several transparent media. Refraction occurs whenever light travels from one medium to another with a different refractive index.

    In the human eye, the two most significant structures responsible for converging (refracting) light are:

    1. The Cornea: This is the clear, front surface of the eye. It provides the majority of the eye's optical power (about two-thirds of the total refractive power). Because the light travels from the air into the denser tissue of the cornea, a significant amount of bending occurs here.
    2. The Crystalline Lens: Located behind the iris, the lens provides the remaining one-third of the refractive power. Its primary role is "accommodation"—it changes shape to fine-tune the focus, allowing the eye to see objects clearly at varying distances.

    While the aqueous humor and vitreous humor are transparent and allow light to pass through, their refractive power is significantly lower compared to the cornea and the lens.

    Step-by-Step Solution

    1. Identify the path of light: Light enters through the cornea, passes through the aqueous humor, goes through the pupil/lens, passes through the vitreous humor, and hits the retina.
    2. Evaluate refractive power: • Cornea: High refractive index change (Air to Cornea). This is the primary refractive element. • Lens: Adjustable refractive index. This is the secondary refractive element. • Aqueous/Vitreous Humors: These are mostly fluid and have refractive indices very close to water; they contribute very little to the actual bending of light compared to the solid structures.
    3. Conclusion: The cornea and the lens are the two main components that perform the bulk of the light refraction required for vision.

    Correct Option

    Comparing this to your options, Option A correctly identifies the two primary refractive structures.

    Exam Tip

    Think of the eye as a camera: the cornea acts like the fixed front glass element of a lens, while the crystalline lens acts like the adjustable zoom/focus ring. Both are essential for getting a sharp image on the "film" (the retina).

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59. 59.

    The device that operates using the magnetic effect of electric current is

    1. A.Rheostat
    2. B.Thermostat
    3. C.Electric bell
    4. D.Carbon microphone

    Show answer

    Answer: C. Electric bell

    AI explanation

    Analysis

    The question asks us to identify which of the listed devices functions based on the magnetic effect of electric current (also known as electromagnetism).

    Concept Explanation

    When an electric current flows through a conductor, it creates a magnetic field around it. This principle is the foundation of electromagnetism. Devices that utilize this effect typically use an electromagnet—a coil of wire wrapped around a soft iron core that becomes magnetized only when current flows through it.

    Let's evaluate the options:

    • A. Rheostat: This is a variable resistor used to control the flow of current in a circuit. It operates based on the principle of resistance, not magnetism.
    • B. Thermostat: This is a device used to maintain a constant temperature. It typically operates based on the principle of thermal expansion of metals (bimetallic strips).
    • C. Electric bell: This device contains an electromagnet. When the switch is pressed, current flows through the coil, creating a magnetic field that attracts a soft iron armature, causing the hammer to strike the bell. Once the circuit is broken, the magnetism ceases, and the process repeats.
    • D. Carbon microphone: This device converts sound waves into electrical signals based on changes in electrical resistance caused by pressure on carbon granules.

    Step-by-Step Solution

    1. Identify the core principle: We are looking for a device that converts electrical energy into mechanical movement using magnetism.
    2. Examine the Electric Bell: An electric bell uses an electromagnet to pull a clapper against a gong. Without the magnetic effect of the current, the clapper would not move.
    3. Eliminate others: The Rheostat (Resistance), Thermostat (Thermal expansion), and Carbon microphone (Variable resistance) do not rely on the magnetic effect of current for their primary operation.
    4. Conclusion: The electric bell is the classic example of an application of the magnetic effect of electric current in physics.

    Answer

    The correct option is C.

    Exam Tip

    Whenever you see a question about the "magnetic effect of current," look for devices that involve movement or switching caused by electricity, such as electric bells, electric motors, relays, or circuit breakers. These are the most common examples tested in JAMB Physics.

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60. 60.

    If 10 objects, tinsels are placed between the mirror of a Kaleidoscope with an inclination of 30º, how many images are formed?

    1. A.110
    2. B.181
    3. C.142
    4. D.210

    Show answer

    Answer: A. 110

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61. 61.

    Water waves and light waves differ generally in their

    1. A.ability to be diffracted
    2. B.ability to be reflected
    3. C.direction of vibration
    4. D.medium of propagation

    Show answer

    Answer: D. medium of propagation

    AI explanation

    Analysis

    To solve this question, we need to compare the fundamental characteristics of mechanical waves (like water waves) and electromagnetic waves (like light waves).

    Concept Explanation

    1. Water Waves (Mechanical Waves): These require a physical medium (water) to travel. Without the water molecules to oscillate and transfer energy, the wave cannot exist.
    2. Light Waves (Electromagnetic Waves): These do not require a material medium. They can travel through a vacuum (like the space between the sun and the earth) as well as through transparent media like glass or water.
    3. Wave Properties: Both water waves and light waves share common wave properties such as reflection, refraction, diffraction, and interference. Therefore, these properties cannot be used to distinguish between them.

    Step-by-Step Solution

    • Step 1: Evaluate Option A (Diffraction). Both light and water waves undergo diffraction (bending around obstacles). This is a similarity, not a difference.
    • Step 2: Evaluate Option B (Reflection). Both light and water waves can be reflected off surfaces. This is also a similarity.
    • Step 3: Evaluate Option C (Direction of vibration). While water waves are transverse and light waves are also transverse, the nature of the vibration differs (mechanical displacement vs. oscillating electric and magnetic fields). However, this is often considered a technicality compared to the most fundamental difference.
    • Step 4: Evaluate Option D (Medium of propagation). This is the most significant difference. Water waves must have a medium, while light waves do not require one. This is the defining characteristic that separates mechanical waves from electromagnetic waves.

    Conclusion

    Water waves are mechanical waves requiring a medium, whereas light waves are electromagnetic and can propagate through a vacuum.

    Exam Tip

    When you see questions comparing wave types, remember the acronym "ME":

    • Mechanical waves (Sound, Water) need a Medium.
    • Electromagnetic waves (Light, X-rays, Radio waves) do not need a medium (they travel through the Ether/Vacuum).

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62. 62.

    When a spiral spring is compressed by an external force of 200 N, it stores 0.16 J of energy. What amount of energy will it store when compressed by an external force of 700 N?

    1. A.1.12J
    2. B.0.48J
    3. C.1.96J
    4. D.O.84J

    Show answer

    Answer: C. 1.96J

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63. 63.

    Calculate the decay constant of a radioactive isotope of half-life 138.5 s.

    1. A.5.0 × 10$^{-3}$ s$^{-1}$
    2. B.5.1 × 10$^{-3}$ s$^{-1}$
    3. C.4.9 × 10$^{-3}$ s$^{-1}$
    4. D.5.2 × 10$^{-3}$ s$^{-1}$

    Show answer

    Answer: A. 5.0 × 10$^{-3}$ s$^{-1}$

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64. 64.

    What mass of silver is deposited during electrolysis when a current of 0.8 A flows for 25 minutes?

    1. A.0.22 g
    2. B.1.86 g
    3. C.0.14 g
    4. D.1.34g

    Show answer

    Answer: D. 1.34g

    AI explanation

    Analysis

    To solve this problem, we use Faraday’s First Law of Electrolysis, which states that the mass ($m$) of a substance deposited during electrolysis is directly proportional to the quantity of electricity ($Q$) passed through the electrolyte.

    Concept

    The formula is:

    $m = \frac{ItM}{nF}$

    Where:

    • $m$ = mass deposited (in grams)
    • $I$ = current (in Amperes) = $0.8\text{ A}$
    • $t$ = time (in seconds) = $25\text{ minutes} \times 60 = 1500\text{ seconds}$
    • $M$ = Molar mass of Silver (Ag) $\approx 108\text{ g/mol}$
    • $n$ = Valency of Silver = $1$ (since $\text{Ag}^+ + e^- \rightarrow \text{Ag}$)
    • $F$ = Faraday’s constant $\approx 96,500\text{ C/mol}$

    Step-by-Step Solution

    1. Calculate the quantity of electricity ($Q$): $Q = I \times t$ $Q = 0.8\text{ A} \times 1500\text{ s} = 1200\text{ Coulombs}$

    2. Apply the formula: $m = \frac{Q \times M}{n \times F}$ $m = \frac{1200 \times 108}{1 \times 96500}$

    3. Perform the calculation: $m = \frac{129600}{96500}$ $m \approx 1.343\text{ g}$

    Rounding to two decimal places, we get 1.34 g.

    Conclusion

    Comparing our result to the options provided, the calculated mass matches option D.

    Exam Tip: Always remember to convert time from minutes to seconds before plugging it into the formula. Many students lose marks by forgetting the $\times 60$ conversion! Also, keep the Faraday constant ($96,500\text{ C}$) in your memory as it is a standard value in JAMB Physics and Chemistry.

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65. 65.

    What is the electrolyte used in wet Leclanche cell

    1. A.Nickle hydroxide
    2. B.Lead dioxide
    3. C.Ammonium chloride
    4. D.Carbon

    Show answer

    Answer: C. Ammonium chloride

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66. 66.

    If the critical angle for a glass–air boundary is 45º, what is the refractive index of the glass?

    1. A.$\sqrt{2}$
    2. B.$\sqrt{5}$
    3. C.$\sqrt{3}$
    4. D.2$\sqrt{2}$

    Show answer

    Answer: A. $\sqrt{2}$

    AI explanation

    Analysis

    The question asks for the refractive index of glass, given the critical angle at a glass-air boundary. This is a classic optics problem involving Snell's Law as it relates to total internal reflection.

    Concept

    The critical angle ($c$) is the angle of incidence in a denser medium for which the angle of refraction in the less dense medium is 90º. The relationship between the refractive index ($n$) and the critical angle ($c$) is given by the formula:

    $n = \frac{1}{\sin(c)}$

    Where:

    • $n$ is the refractive index of the denser medium (glass).
    • $c$ is the critical angle.

    Solution

    1. Identify the given values: • Critical angle ($c$) = 45º

    2. Apply the formula: $$n = \frac{1}{\sin(45^\circ)}$$

    3. Recall the trigonometric value: We know from standard trigonometric ratios that $\sin(45^\circ) = \frac{1}{\sqrt{2}}$ (or $\frac{\sqrt{2}}{2}$).

    4. Calculate $n$: $$n = \frac{1}{\frac{1}{\sqrt{2}}}$$ $$n = \sqrt{2}$$

    Conclusion

    The refractive index of the glass is $\sqrt{2}$. This matches option A.

    Exam Tip

    Always remember that the refractive index ($n$) is always greater than 1. If you ever calculate a value less than 1, check your math! Also, for common angles like 30º, 45º, and 60º, memorizing their sine values will save you precious time during your JAMB exam.

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67. 67.

    A collection of condensed suspended dust particles in the air constitute

    1. A.Cloud
    2. B.fog
    3. C.Mist
    4. D.Rain

    Show answer

    Answer: A. Cloud

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68. 68.

    A machine has an efficiency of 80%. If the input work is 200J, the output work is?

    1. A.250J
    2. B.160J
    3. C.120J
    4. D.100J

    Show answer

    Answer: B. 160J

    AI explanation

    1. Analyze the question

    We are given the efficiency of a machine and the input work. We need to calculate the actual work output produced by the machine.

    2. Explain the concept

    Efficiency ($\eta$) is defined as the ratio of the useful work output to the total work input, expressed as a percentage. The formula is:

    $\text{Efficiency} = \left( \frac{\text{Work Output}}{\text{Work Input}} \right) \times 100\%$

    To find the work output, we rearrange the formula:

    $\text{Work Output} = \frac{\text{Efficiency} \times \text{Work Input}}{100}$

    3. Show the solution

    • Given: • Efficiency ($\eta$) = 80% • Work Input = 200J

    • Calculation: $$\text{Work Output} = \frac{80}{100} \times 200\text{J}$$ $$\text{Work Output} = 0.8 \times 200\text{J}$$ $$\text{Work Output} = 160\text{J}$$

    4. Identify the answer

    Comparing our result to the given options, 160J corresponds to option B.

    5. Exam Tip

    Always remember that for any real machine, the efficiency must be less than 100% because some energy is always lost to friction or heat. If your calculation results in an output work higher than the input work, you have likely multiplied instead of divided by the efficiency percentage!

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69. 69.

    Using the oscillating simple pendulum above, the maximum kinetic energy is obtained at

    1. A.Q
    2. B.S
    3. C.R
    4. D.P

    Show answer

    Answer: A. Q

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70. 70.

    A boy uses a single string pulley system to lift a mass of 20kg moving with a velocity of 5ms$^{-1}$. What is the power developed by the boy if g = 10ms$^{-2}$?

    1. A.100W
    2. B.1000W
    3. C.250W
    4. D.40W

    Show answer

    Answer: B. 1000W

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71. 71.

    The gravitational pull between two bodies is 20N. Find the gravitational pull when their distance of separation is doubled.

    1. A.10N
    2. B.5N
    3. C.13N
    4. D.20N

    Show answer

    Answer: B. 5N

    AI explanation

    1. Analyze the Question

    We are given the initial gravitational force between two bodies and asked to find the new force when the distance between them is doubled. This is a classic application of Newton's Law of Universal Gravitation.

    2. Explain the Concept

    Newton’s Law of Universal Gravitation states that the force ($F$) between two bodies is directly proportional to the product of their masses ($m_1$ and $m_2$) and inversely proportional to the square of the distance ($r$) between them:

    $F = \frac{G m_1 m_2}{r^2}$

    From this formula, we can see that $F \propto \frac{1}{r^2}$. This means if the distance $r$ changes, the force $F$ changes by the square of that factor.

    3. Show the Solution

    • Initial state: $F_1 = 20\text{N}$ at distance $r_1 = r$.
    • Final state: $r_2 = 2r$ (the distance is doubled).

    Using the proportionality $F \propto \frac{1}{r^2}$:

    $\frac{F_2}{F_1} = \frac{r_1^2}{r_2^2}$

    Substitute the values:

    $\frac{F_2}{20} = \frac{r^2}{(2r)^2}$

    $\frac{F_2}{20} = \frac{r^2}{4r^2}$

    The $r^2$ terms cancel out:

    $\frac{F_2}{20} = \frac{1}{4}$

    Now, solve for $F_2$:

    $F_2 = \frac{20}{4}$

    $F_2 = 5\text{N}$

    4. Identify the Answer

    The calculation shows that when the distance is doubled, the force becomes one-fourth of the original value. Therefore, the correct option is B.

    5. Exam Tip

    Whenever you see "distance is doubled" in an inverse-square law problem (like Gravitation or Electrostatics/Coulomb's Law), remember the "Inverse Square Rule":

    • If distance is doubled ($2r$), force becomes $1/2^2 = 1/4$ of the original.
    • If distance is tripled ($3r$), force becomes $1/3^2 = 1/9$ of the original.
    • If distance is halved ($1/2r$), force becomes $1/(1/2)^2 = 4$ times the original.

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72. 72.

    What colour has the lowest frequency in the spectrum of white light?

    1. A.Red
    2. B.Yellow
    3. C.Indigo
    4. D.Blue

    Show answer

    Answer: A. Red

    AI explanation

    Analysis

    The question asks for the color with the lowest frequency within the visible spectrum of white light. To solve this, we must understand the relationship between frequency, wavelength, and the dispersion of light.

    Concept Explanation

    When white light is dispersed (split) into its component colors, it forms the spectrum known by the acronym ROYGBIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet).

    In physics, the wave equation is given by:

    $v = f \lambda$

    Where:

    • $v$ = speed of light (constant in a vacuum)
    • $f$ = frequency
    • $\lambda$ (lambda) = wavelength

    Because the speed of light ($v$) is constant, frequency ($f$) and wavelength ($\lambda$) are inversely proportional. This means that the color with the longest wavelength will have the lowest frequency.

    In the visible spectrum:

    • Red light has the longest wavelength (approximately 700 nm).
    • Violet light has the shortest wavelength (approximately 400 nm).

    Since Red has the longest wavelength, it must have the lowest frequency.

    Step-by-Step Solution

    1. Recall the spectrum order: The colors are arranged by increasing frequency (or decreasing wavelength) as follows: Red $\rightarrow$ Orange $\rightarrow$ Yellow $\rightarrow$ Green $\rightarrow$ Blue $\rightarrow$ Indigo $\rightarrow$ Violet.
    2. Identify the extremes: Red is at one end (lowest frequency, longest wavelength) and Violet is at the other end (highest frequency, shortest wavelength).
    3. Compare the options: • Red: Lowest frequency • Yellow: Higher frequency than Red • Blue: Higher frequency than Red and Yellow • Indigo: Higher frequency than Red, Yellow, and Blue
    4. Conclusion: Red is the color with the lowest frequency.

    Exam Tip

    Remember the mnemonic ROYGBIV. Just keep in mind that Red is like a "lazy" wave—it is long and slow (low frequency), while Violet is a "busy" wave—it is short and fast (high frequency). This will help you remember the relationship between frequency and color every time!

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73. 73.

    Which of the following electromagnetic spectra has the shortest wavelength?

    1. A.Ultra violet radiation
    2. B.X - rays
    3. C.Visible light
    4. D.Infrared

    Show answer

    Answer: B. X - rays

    AI explanation

    Analysis

    The question asks you to identify which of the listed electromagnetic radiations has the shortest wavelength. To answer this, we must recall the electromagnetic spectrum and the relationship between wavelength, frequency, and energy.

    Concept Explanation

    The electromagnetic spectrum is a range of waves arranged in order of increasing frequency and decreasing wavelength. The general order from longest wavelength (lowest frequency) to shortest wavelength (highest frequency) is:

    1. Radio waves (Longest wavelength)
    2. Microwaves
    3. Infrared
    4. Visible light
    5. Ultraviolet (UV)
    6. X-rays
    7. Gamma rays (Shortest wavelength)

    Key Principle: Wavelength ($\lambda$) and frequency ($f$) are inversely proportional according to the formula $c = f\lambda$ (where $c$ is the speed of light). Therefore, as you move toward the high-energy end of the spectrum (X-rays and Gamma rays), the wavelength becomes significantly shorter.

    Step-by-Step Solution

    1. Compare the given options: • Infrared: Longer wavelength than visible light. • Visible light: Longer wavelength than UV. • Ultraviolet: Longer wavelength than X-rays. • X-rays: Located at the high-frequency end of this specific list.

    2. Evaluate the positions: Looking at the spectrum order, X-rays appear after Ultraviolet and Visible light. Since wavelength decreases as we move from Infrared toward X-rays, X-rays must have the shortest wavelength among the options provided.

    Conclusion

    Comparing the options provided, X-rays have the highest frequency and, consequently, the shortest wavelength.

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

    • Radio
    • Microwaves
    • Infrared
    • Visible
    • Ultraviolet
    • X-rays
    • Gamma rays As you move from left to right, the wavelength gets shorter!

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74. 74.

    5400kJ of heat energy was lost when some amount of steam condensed to water for drinking purposes at 15º C. What is the quantity of water collected? [L$_f$ = 2.26 × 10$^6$ Jkg$^{-1}$, c$_w$ = 4200 Jkg$^{-1}K^{-1}$]

    1. A.0.95 kg
    2. B.8.24 kg
    3. C.1.84 kg
    4. D.2.06 kg

    Show answer

    Answer: D. 2.06 kg

    AI explanation

    1. Analyze the Question

    We are given the total heat energy lost ($Q_{total} = 5400 \text{ kJ} = 5,400,000 \text{ J}$) during a process where steam at $100^\circ\text{C}$ condenses into water and then cools down to $15^\circ\text{C}$. We need to find the mass ($m$) of the water collected.

    2. Explain the Concept

    The total heat lost involves two stages:

    1. Phase Change (Latent Heat): The steam at $100^\circ\text{C}$ turns into water at $100^\circ\text{C}$. The formula is $Q_1 = mL_v$. (Note: The question provides $L_f$, which usually denotes latent heat of fusion, but in the context of steam condensing, we use the latent heat of vaporization, $L_v = 2.26 \times 10^6 \text{ J/kg}$.)
    2. Temperature Change (Sensible Heat): The water cools from $100^\circ\text{C}$ to $15^\circ\text{C}$. The formula is $Q_2 = mc\Delta\theta$.

    Total heat $Q_{total} = Q_1 + Q_2 = m(L_v + c\Delta\theta)$.

    3. Show the Solution

    • Step 1: Identify the variables • $Q_{total} = 5,400,000 \text{ J}$ • $L_v = 2.26 \times 10^6 \text{ J/kg}$ • $c_w = 4200 \text{ J/kgK}$ • $\Delta\theta = 100^\circ\text{C} - 15^\circ\text{C} = 85^\circ\text{C}$

    • Step 2: Set up the equation $5,400,000 = m(2,260,000 + (4200 \times 85))$

    • Step 3: Calculate the values inside the bracket $4200 \times 85 = 357,000$ $2,260,000 + 357,000 = 2,617,000$

    • Step 4: Solve for $m$ $m = \frac{5,400,000}{2,617,000}$ $m \approx 2.0634 \text{ kg}$

    4. Identify the Answer

    Rounding to two decimal places, we get $2.06 \text{ kg}$. This matches option D.

    5. Tip

    When dealing with phase changes, always check if the substance is changing temperature after the phase change. If it is, you must add the sensible heat ($mc\Delta\theta$) to the latent heat ($mL$). Don't forget to convert kilojoules (kJ) to joules (J) by multiplying by 1000 before starting your calculation!

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75. 75.

    If the weight of an object on the Earth's surface is 2.5 x 10$^3$N, what is its weight on the moon's surface if the gravitational force of the moon is one-sixth of the Earth's(g = 10m/s$^{-2}$)

    1. A.360.87N
    2. B.416.67N
    3. C.214.49N
    4. D.510.79N

    Show answer

    Answer: B. 416.67N

    AI explanation

    Analysis

    The question asks us to calculate the weight of an object on the Moon, given its weight on Earth and the relationship between the gravitational pull of the Moon and the Earth.

    Concept

    Weight ($W$) is the force of gravity acting on an object's mass ($m$). It is calculated using the formula: $W = mg$ where $g$ is the acceleration due to gravity.

    Since the mass ($m$) of an object remains constant regardless of its location, the weight of an object on the Moon ($W_m$) is directly proportional to the gravitational acceleration on the Moon ($g_m$). Given that $g_m = \frac{1}{6} g_e$ (where $g_e$ is gravity on Earth), it follows that: $W_m = \frac{1}{6} W_e$

    Solution

    1. Identify the given values: • Weight on Earth ($W_e$) = $2.5 \times 10^3\text{ N} = 2500\text{ N}$ • Gravitational relationship: $g_m = \frac{1}{6} g_e$

    2. Apply the formula: $W_m = \frac{W_e}{6}$ $W_m = \frac{2500}{6}$

    3. Calculate the result: $W_m = 416.666... \text{ N}$ Rounding to two decimal places, we get 416.67 N.

    Conclusion

    Comparing our result to the provided options, the correct value is 416.67 N.

    Exam Tip

    Always remember that mass is a scalar quantity that stays the same everywhere in the universe, while weight is a vector quantity (a force) that changes depending on the gravitational field strength of the location. If a question asks for mass, ensure you divide the weight by $g$ ($10\text{ m/s}^2$) first!

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76. 76.

    The graphical representation of the pressure law is always a straight line passing through the origin, only if the temperature scale is

    1. A.Rankine
    2. B.Celsius
    3. C.Fahrenheit
    4. D.thermodynamic

    Show answer

    Answer: D. thermodynamic

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77. 77.

    A refrigerator uses 150W. If it is kept on for 336 hours nonstop. What is the energy consumed in Kwh?

    1. A.60.20Kwh
    2. B.25.01Kwh
    3. C.50.40Kwh
    4. D.30.20Kwh

    Show answer

    Answer: C. 50.40Kwh

    AI explanation

    Analysis

    To solve this problem, we need to calculate the total electrical energy consumed by the refrigerator. The energy consumed is the product of the power rating of the appliance and the time for which it is used.

    Concept

    The formula for electrical energy ($E$) is:

    $E = P \times t$

    Where:

    • $P$ is the power in Watts (W)
    • $t$ is the time in hours (h)
    • $E$ is the energy in Watt-hours (Wh)

    Since the question asks for the answer in Kilowatt-hours (kWh), we must convert the power from Watts to Kilowatts by dividing by 1,000.

    Step-by-Step Solution

    Step 1: Convert Power from Watts to Kilowatts

    $P = 150 \text{ W}$

    $P (\text{in kW}) = \frac{150}{1000} = 0.15 \text{ kW}$

    Step 2: Identify the time

    $t = 336 \text{ hours}$

    Step 3: Calculate the energy in kWh

    $E = P (\text{in kW}) \times t (\text{in hours})$

    $E = 0.15 \text{ kW} \times 336 \text{ h}$

    $E = 50.40 \text{ kWh}$

    Conclusion

    Comparing our result to the given options, we can see that the calculated value matches option C.

    Exam Tip: Always check the units requested in the question. JAMB often tests your ability to convert units (like Watts to Kilowatts or minutes to hours). If you had calculated in Watt-hours first ($150 \times 336 = 50,400 \text{ Wh}$), remember to divide by 1,000 to get the final answer in kWh.

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78. 78.

    One of the following is not a radiation detector

    1. A.Electrophorus
    2. B.Scintillation chamber
    3. C.Geiger muller counter
    4. D.Film badge

    Show answer

    Answer: A. Electrophorus

    AI explanation

    Analysis

    The question asks us to identify which of the listed devices is not used for detecting ionizing radiation. To solve this, we must evaluate the function of each device in the context of nuclear physics.

    Concept Explanation

    Radiation detectors are instruments designed to detect, track, and/or identify high-energy particles, such as those produced by nuclear decay, cosmic radiation, or reactions in a nuclear reactor.

    • Scintillation chamber: Uses a scintillator (a material that exhibits luminescence when struck by ionizing radiation) to detect radiation.
    • Geiger-Muller (GM) counter: Uses a gas-filled tube to detect ionizing radiation by creating an electrical pulse when radiation ionizes the gas inside.
    • Film badge: A personal dosimeter used to monitor cumulative radiation exposure. The radiation darkens the photographic film inside the badge, which is later developed to measure the dose.
    • Electrophorus: This is an early electrostatic generator used to produce static electricity through the principle of electrostatic induction. It has no mechanism for detecting or measuring nuclear radiation.

    Step-by-Step Solution

    1. Evaluate Option B (Scintillation chamber): This is a well-known radiation detector used in laboratories to measure radioactivity.
    2. Evaluate Option C (Geiger-Muller counter): This is the most common device used to detect alpha, beta, and gamma radiation.
    3. Evaluate Option D (Film badge): This is a standard safety device worn by radiographers and nuclear workers to measure radiation exposure.
    4. Evaluate Option A (Electrophorus): An electrophorus consists of a dielectric plate and a metal plate with an insulating handle. It is used to generate high-voltage static charges, not to detect radiation.

    Since the electrophorus is an electrostatic device and not a radiation detector, it is the correct answer.

    Conclusion

    The correct option is A.

    Exam Tip

    When you see "not" in a question, underline it immediately! It is easy to accidentally pick the first correct detector you see (like the Geiger-Muller counter) if you aren't careful. Always scan all options before finalizing your choice.

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

80. 80.

    What form of energy is present in the food we eat?

    1. A.Kinetic
    2. B.Mechanical
    3. C.Potential
    4. D.Chemical

    Show answer

    Answer: D. Chemical

    AI explanation

    Analysis

    The question asks us to identify the specific form of energy stored within food substances. In physics and biology, we look at how energy is held within the molecular structure of matter before it is released for use by the body.

    Concept Explanation

    Energy exists in many forms, but it is categorized based on how it is stored or transferred:

    • Kinetic Energy: The energy an object possesses due to its motion.
    • Mechanical Energy: The sum of potential and kinetic energy in a system (often associated with machines or moving objects).
    • Potential Energy: Stored energy based on an object's position or state (like a stretched rubber band).
    • Chemical Energy: Energy stored in the bonds of chemical compounds (atoms and molecules). When these bonds are broken during metabolic processes (like digestion and respiration), the energy is released to perform work, such as moving muscles or maintaining body temperature.

    Step-by-Step Solution

    1. Examine the nature of food: Food consists of organic molecules like carbohydrates, proteins, and fats.
    2. Analyze the storage: These molecules are held together by chemical bonds. The energy is not "moving" (kinetic) while the food is on your plate, nor is it purely gravitational potential energy.
    3. Identify the release mechanism: When you eat, your body performs chemical reactions (cellular respiration) to break these bonds. This process releases the energy stored within those bonds.
    4. Conclusion: Because the energy is locked within the molecular bonds of the food, it is classified as chemical energy.

    Tip for JAMB

    Whenever you see questions about energy in "batteries," "fuels," or "food," the answer is almost always Chemical Energy. Think of these as "energy reservoirs" where the energy is waiting to be released through a chemical reaction.

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

82. 82.

    The figure shows a uniform metre rule of weight 100 N balanced by a knife edge at the 10 cm mark and a cord attached at the 85 cm mark. What is the tension in the string?

    1. A.23.62 N
    2. B.53.33 N
    3. C.35.74 N
    4. D.78.68 N

    Show answer

    Answer: B. 53.33 N

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83. 83.

    The density of water is 1g/cm$^3$ while that of ice is 0.9g/cm$^3$. Calculate the change in volume when 90g of ice is completely melted.

    1. A.9cm$^3$
    2. B.90cm$^3$
    3. C.0cm$^3$
    4. D.10cm$^3$

    Show answer

    Answer: D. 10cm$^3$

    AI explanation

    Analysis

    To solve this problem, we need to calculate the volume of the ice before it melts and the volume of the water after it melts. The "change in volume" is the difference between these two values.

    Concept

    The relationship between density ($\rho$), mass ($m$), and volume ($V$) is given by the formula:

    $\rho = \frac{m}{V} \implies V = \frac{m}{\rho}$

    Step-by-Step Solution

    Step 1: Calculate the volume of 90g of ice ($V_{ice}$) Using the density of ice ($\rho_{ice} = 0.9 \, \text{g/cm}^3$):

    $V_{ice} = \frac{\text{mass}}{\rho_{ice}} = \frac{90 \, \text{g}}{0.9 \, \text{g/cm}^3}$

    $V_{ice} = 100 \, \text{cm}^3$

    Step 2: Calculate the volume of the resulting water ($V_{water}$) When ice melts, its mass remains constant (Law of Conservation of Mass). So, we still have 90g of water. Using the density of water ($\rho_{water} = 1 \, \text{g/cm}^3$):

    $V_{water} = \frac{\text{mass}}{\rho_{water}} = \frac{90 \, \text{g}}{1 \, \text{g/cm}^3}$

    $V_{water} = 90 \, \text{cm}^3$

    Step 3: Calculate the change in volume ($\Delta V$)

    $\Delta V = V_{ice} - V_{water}$

    $\Delta V = 100 \, \text{cm}^3 - 90 \, \text{cm}^3$

    $\Delta V = 10 \, \text{cm}^3$

    Conclusion

    The volume decreases by 10 cm³ as the ice melts into water. Comparing this to your options, the correct choice is D.

    Exam Tip

    Always remember that water is unique: it is one of the few substances that contracts when it melts from ice to liquid. If you ever get a negative result for a change in volume question involving ice melting, don't panic—it just means the volume decreased! Always double-check your units to ensure they are consistent (g/cm³ and g).

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84. 84.

    The dimensional symbol of tension in a string is expressed as

    1. A.L T$^{-2}$
    2. B.M$^2$ L$^{-1}$ T$^{-2}$
    3. C.M L T$^2$
    4. D.M L T$^{-2}$

    Show answer

    Answer: D. M L T$^{-2}$

    AI explanation

    Analysis

    The question asks for the dimensional formula of tension. To solve this, we must recognize that tension is a type of force. In physics, any force (whether it is tension, weight, thrust, or friction) follows the same dimensional rules.

    Concept

    According to Newton's Second Law of Motion, Force ($F$) is the product of mass ($m$) and acceleration ($a$):

    $F = m \times a$

    • Mass ($m$): The dimension is represented by [M].
    • Acceleration ($a$): Acceleration is the rate of change of velocity with respect to time. Since velocity is distance/time ($L/T$), acceleration is distance/time$^2$ ($L/T^2$). Therefore, the dimension is [L T$^{-2}$].

    Solution

    1. Since Tension ($T$) is a force, we use the formula: $$\text{Tension} = \text{Mass} \times \text{Acceleration}$$
    2. Substitute the dimensions: $$\text{Dimension} = [M] \times [L T^{-2}]$$
    3. Combine them: $$\text{Dimension} = [M L T^{-2}]$$

    Comparing this result to the given options:

    • A: $L T^{-2}$ (This is acceleration)
    • B: $M^2 L^{-1} T^{-2}$ (Incorrect)
    • C: $M L T^2$ (Incorrect)
    • D: $M L T^{-2}$ (Correct)

    Tip for JAMB

    Whenever you are asked for the dimension of a force-related quantity (like Tension, Weight, Thrust, or Upthrust), always remember the acronym MLT with the exponent -2 on the T. It is a common JAMB favorite!

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85. 85.

    The focal length of the natural eye lens is variable due to the action of the

    1. A.Optical fluid
    2. B.Ciliary muscle
    3. C.Vitreous humor
    4. D.retina nerves

    Show answer

    Answer: B. Ciliary muscle

    AI explanation

    Analysis of the Question

    The question asks for the specific part of the human eye responsible for changing the focal length of the lens. This process, known as accommodation, allows the eye to focus on objects at varying distances (near and far).

    Explanation of the Concept

    The human eye functions similarly to a camera. To focus on objects at different distances, the eye must adjust its refractive power.

    • The Lens: The crystalline lens is flexible.
    • Accommodation: When you look at a near object, the lens needs to become more convex (thicker) to increase its refractive power. When you look at a distant object, the lens flattens to decrease its power.
    • Ciliary Muscles: These are circular muscles attached to the lens by suspensory ligaments. By contracting or relaxing, these muscles change the tension on the ligaments, which in turn alters the shape (and therefore the focal length) of the lens.

    Step-by-Step Solution

    1. Evaluate Option A (Optical fluid): Fluids like the aqueous and vitreous humor provide shape and pressure to the eye but do not actively change the shape of the lens.
    2. Evaluate Option B (Ciliary muscle): These muscles are directly responsible for the mechanical adjustment of the lens shape. Their contraction/relaxation is the fundamental mechanism of accommodation.
    3. Evaluate Option C (Vitreous humor): This is the jelly-like substance filling the main cavity of the eyeball. It maintains the eyeball's shape but plays no role in adjusting the lens's focal length.
    4. Evaluate Option D (Retina nerves): The retina is the light-sensitive layer at the back of the eye. It converts light into electrical signals to be sent to the brain; it does not control the physical shape of the lens.

    Conclusion

    The ciliary muscles are the active components that adjust the curvature of the lens, thereby varying the focal length of the eye.

    Exam Tip

    Think of the Ciliary Muscles as the "focus ring" on a camera lens. Just as you twist the ring to focus a camera, your ciliary muscles "squeeze" or "stretch" your eye lens to focus on what you are reading or looking at!

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86. 86.

    If the specific gravity of a liquid is 0.76, calculate its density(($\rho_w$ = 1000Kgm$^{-3}$)

    1. A.760Kgm$^{-3}$
    2. B.76Kgm$^{-3}$
    3. C.7.6Kgm$^{-3}$
    4. D.7600Kgm$^{-3}$

    Show answer

    Answer: A. 760Kgm$^{-3}$

    AI explanation

    1. Analyze the question

    You are asked to find the density of a liquid given its specific gravity (also known as relative density) and the density of water.

    2. Explain the concept

    Specific Gravity (Relative Density) is a dimensionless quantity defined as the ratio of the density of a substance to the density of a reference substance (usually water).

    The formula is:

    $\text{Specific Gravity} = \frac{\text{Density of substance}}{\text{Density of water}}$

    To find the density of the substance, we rearrange the formula:

    $\text{Density of substance} = \text{Specific Gravity} \times \text{Density of water}$

    3. Show the solution

    • Given: • Specific Gravity = 0.76 • Density of water ($\rho_w$) = 1000 kgm⁻³

    • Calculation: $$\text{Density of liquid} = 0.76 \times 1000 \text{ kgm}^{-3}$$ $$\text{Density of liquid} = 760 \text{ kgm}^{-3}$$

    4. Identify the answer

    Comparing our result to the given options: A. 760 kgm⁻³ B. 76 kgm⁻³ C. 7.6 kgm⁻³ D. 7600 kgm⁻³

    The correct option is A.

    5. Tip

    When dealing with specific gravity, remember that it is just a multiplier. If you are converting from specific gravity to density in SI units (kgm⁻³), simply multiply by 1000. If you are converting to CGS units (gcm⁻³), the specific gravity value is numerically equal to the density (e.g., 0.76 gcm⁻³). This is a quick way to verify your work during the exam!

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87. 87.

    What magnitude of electric current can store 2.5 J of energy in a 3 H induction coil?

    1. A.1.29 A
    2. B.2.48 A
    3. C.5.00 A
    4. D.3.66 A

    Show answer

    Answer: A. 1.29 A

    AI explanation

    Analysis

    The question asks for the magnitude of electric current ($I$) that results in a specific amount of energy ($E$) being stored in an inductor with a given inductance ($L$).

    Concept

    The energy stored in an inductor is given by the formula:

    $E = \frac{1}{2}LI^2$

    Where:

    • $E$ = Energy stored in Joules (J)
    • $L$ = Inductance in Henrys (H)
    • $I$ = Current in Amperes (A)

    Step-by-Step Solution

    1. Identify the given values: • $E = 2.5\text{ J}$ • $L = 3\text{ H}$

    2. Rearrange the formula to solve for $I$: $$2E = LI^2$$ $$I^2 = \frac{2E}{L}$$ $$I = \sqrt{\frac{2E}{L}}$$

    3. Substitute the values into the equation: $$I = \sqrt{\frac{2 \times 2.5}{3}}$$ $$I = \sqrt{\frac{5}{3}}$$ $$I = \sqrt{1.666...}$$

    4. Calculate the final value: $$I \approx 1.29099\text{ A}$$

    Rounding to two decimal places, we get 1.29 A.

    Conclusion

    Comparing our result to the provided options, the correct value is 1.29 A.

    Exam Tip

    When dealing with energy formulas in physics (like $\frac{1}{2}LI^2$ for inductors or $\frac{1}{2}CV^2$ for capacitors), always remember the "1/2" factor. A common mistake students make is forgetting to multiply the energy by 2 before taking the square root. Also, ensure your units are in SI (Joules and Henrys) before calculating to avoid conversion errors.

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88. 88.

    A short-sighted person's far point is 95cm. The defect can be corrected using

    1. A.Diverging mirror of focal length 95cm
    2. B.Plano convex lens of focal length 90cm
    3. C.Diverging lens of focal length 95cm
    4. D.Converging lens of focal length 95cm

    Show answer

    Answer: C. Diverging lens of focal length 95cm

    AI explanation

    Analysis of the Question

    The question describes a person with short-sightedness (myopia). A person with this defect can see near objects clearly but cannot see distant objects beyond a certain point (the far point). To correct this, we need to use a lens that will take an object at infinity (where a normal eye should see) and form a virtual image at the person's actual far point.

    Concept Explanation

    1. The Defect: Myopia occurs when the eyeball is too long or the lens is too powerful, causing light from distant objects to focus in front of the retina.
    2. The Correction: We use a diverging lens (concave lens) to spread out the light rays before they enter the eye, effectively moving the image back onto the retina.
    3. The Formula: We use the thin lens formula: $$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$ • $u$ (Object distance): Since we want the person to see objects at infinity, $u = \infty$. • $v$ (Image distance): The lens must form a virtual image at the person's far point. Since it is a virtual image, $v = -95\text{ cm}$. • $f$ (Focal length): This is what we need to find.

    Step-by-Step Solution

    1. Substitute the values into the lens formula: $$\frac{1}{f} = \frac{1}{\infty} + \frac{1}{-95}$$
    2. Recall that $\frac{1}{\infty} = 0$: $$\frac{1}{f} = 0 - \frac{1}{95}$$ $$\frac{1}{f} = -\frac{1}{95}$$
    3. Solving for $f$: $$f = -95\text{ cm}$$
    4. The negative sign indicates that the lens is diverging (concave). Therefore, a diverging lens with a focal length of 95 cm is required.

    Conclusion

    Comparing our result to the given options, the correct choice is a diverging lens with a focal length of 95 cm.

    Exam Tip

    Always remember: Myopia is corrected with a Concave (Diverging) lens, and Hypermetropia (long-sightedness) is corrected with a Convex (Converging) lens. A quick mnemonic is "Myopia" has 6 letters, and "Concave" has 7; "Hypermetropia" is a long word, and "Convex" is a short word—or simply remember the acronym "CON-CAVE" for the "near" defect!

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89. 89.

    A wooden block of relative density 0.4 floats in a liquid of density 1600 kg m$^{-3}$. What fraction of its volume is immersed?

    1. A.0.15
    2. B.0.10
    3. C.0.25
    4. D.0.20

    Show answer

    Answer: C. 0.25

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90. 90.

    Calculate the specific heat capacity of a metal rod of mass 0.025kg whose temperature was raised by 15ºC when 1000J of heat energy was added to the rod(assuming the heat loss to the surrounding is negligible)

    1. A.2440.5JKg$^{-1}$K$^{-1}$
    2. B.3000.0JKg$^{-1}$K$^{-1}$
    3. C.2888.4JKg$^{-1}$K$^{-1}$
    4. D.2666.7JKg$^{-1}$K$^{-1}$

    Show answer

    Answer: D. 2666.7JKg$^{-1}$K$^{-1}$

    AI explanation

    Analysis

    To solve this problem, we need to relate the heat energy supplied to a substance with the resulting change in its temperature. This is a classic calorimetry problem involving the specific heat capacity formula.

    Concept

    The formula for heat energy ($Q$) is given by:

    $Q = mc\Delta\theta$

    Where:

    • $Q$ = Heat energy supplied (in Joules, J)
    • $m$ = Mass of the substance (in kilograms, kg)
    • $c$ = Specific heat capacity (in Jkg$^{-1}$K$^{-1}$)
    • $\Delta\theta$ = Change in temperature (in Kelvin or Celsius, as the interval is the same)

    We need to rearrange this formula to solve for the specific heat capacity ($c$):

    $c = \frac{Q}{m \times \Delta\theta}$

    Solution

    Step 1: Identify the given values

    • $Q = 1000\text{ J}$
    • $m = 0.025\text{ kg}$
    • $\Delta\theta = 15^\circ\text{C}$ (Note: A change of $15^\circ\text{C}$ is equivalent to a change of $15\text{ K}$)

    Step 2: Substitute the values into the rearranged formula

    $c = \frac{1000}{0.025 \times 15}$

    Step 3: Perform the calculation

    • First, calculate the denominator: $0.025 \times 15 = 0.375$
    • Now, divide the heat energy by the result: $c = \frac{1000}{0.375}$
    • $c = 2666.666...$

    Rounding to one decimal place, we get $2666.7\text{ Jkg}^{-1}\text{K}^{-1}$.

    Conclusion

    Comparing our result with the given options, it matches option D.

    Exam Tip

    When dealing with specific heat capacity questions, always ensure your mass is in kilograms (kg). If the question gives you the mass in grams (g), you must divide by 1000 before plugging it into the formula. Also, remember that a change in temperature ($\Delta\theta$) in Celsius is numerically identical to a change in Kelvin, so you don't need to add 273 to the temperature change!

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91. 91.

    In electromagnetic induction, the generated electricity is actually a voltage called

    1. A.Induced emf
    2. B.Eddy current
    3. C.Inductor voltage
    4. D.Watts

    Show answer

    Answer: A. Induced emf

    AI explanation

    Analysis

    The question asks for the specific term used to describe the voltage produced in a conductor when it is subjected to a changing magnetic field, a phenomenon governed by Faraday's Law of Electromagnetic Induction.

    Concept Explanation

    Electromagnetic induction occurs when a conductor (like a wire) is moved through a magnetic field, or when the magnetic field around a stationary conductor changes. According to Faraday’s Law, this change in magnetic flux induces an electromotive force (emf) in the conductor.

    • emf (Electromotive Force): This is the energy per unit charge provided by a source (like a battery or an induction process) to drive current around a circuit. Even though it is called "force," it is measured in Volts, just like potential difference.
    • Eddy Current: These are loops of electrical current induced within conductors by a changing magnetic field, but they are the result of the induced emf, not the voltage itself.
    • Inductor Voltage: This usually refers to the potential difference across a component (an inductor) due to its own self-inductance, rather than the general phenomenon of induction.
    • Watts: This is the unit of power, not voltage.

    Step-by-Step Solution

    1. Identify the phenomenon: The process of generating electricity via magnetic fields is Electromagnetic Induction.
    2. Apply Faraday's Law: Faraday's Law states that the magnitude of the induced electromotive force (emf) in a circuit is directly proportional to the rate of change of the magnetic flux through the circuit.
    3. Define the output: The "generated electricity" or "voltage" produced by this process is technically referred to as the Induced electromotive force (emf).
    4. Evaluate the options: • A (Induced emf): This is the standard scientific term for the voltage generated by electromagnetic induction. • B (Eddy current): This is a current, not a voltage. • C (Inductor voltage): Too specific to a component; "Induced emf" is the broader, correct term for the phenomenon. • D (Watts): This is a unit of power.

    Conclusion

    The correct term for the voltage generated during electromagnetic induction is the Induced emf.

    Exam Tip: Whenever you see "Electromagnetic Induction" in a question, always look for keywords like "Faraday," "Lenz's Law," "Magnetic Flux," or "Induced emf." These terms are almost always linked together in JAMB Physics questions.

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

93. 93.

    Without considering the containing vessel, what mass of boiled water can raise the temperature of 8 kg of water from 25°C to 60°C when mixed in a heat-proof container?

    1. A.10kg
    2. B.7kg
    3. C.5kg
    4. D.6kg

    Show answer

    Answer: B. 7kg

    AI explanation

    To solve this problem, we use the Principle of Conservation of Heat Energy (also known as the Method of Mixtures). This principle states that:

    Heat Lost by Hot Water = Heat Gained by Cold Water

    1. Analyze the Question

    • Cold Water: Mass ($m_1$) = 8 kg, Initial Temperature ($T_1$) = 25°C.
    • Hot Water: Mass ($m_2$) = ?, Initial Temperature ($T_2$) = 100°C (Since it is "boiled water," we assume its temperature is 100°C).
    • Final Mixture Temperature ($T_f$): 60°C.
    • Specific Heat Capacity ($c$): Since both substances are water, the specific heat capacity ($c$) is the same for both and will cancel out in the equation.

    2. Explain the Concept

    The formula for heat exchange is:

    $Q = mc\Delta\theta$

    Where:

    • $m$ = mass
    • $c$ = specific heat capacity
    • $\Delta\theta$ = change in temperature

    3. Show the Solution

    Step 1: Calculate heat gained by the cold water:

    $\text{Heat Gained} = m_1 \times c \times (T_f - T_1)$

    $\text{Heat Gained} = 8 \times c \times (60 - 25)$

    $\text{Heat Gained} = 8 \times c \times 35 = 280c$

    Step 2: Calculate heat lost by the hot water:

    $\text{Heat Lost} = m_2 \times c \times (T_2 - T_f)$

    $\text{Heat Lost} = m_2 \times c \times (100 - 60)$

    $\text{Heat Lost} = m_2 \times c \times 40 = 40m_2c$

    Step 3: Equate Heat Lost to Heat Gained:

    $40m_2c = 280c$

    Divide both sides by $c$ (since it is common to both):

    $40m_2 = 280$

    $m_2 = \frac{280}{40}$

    $m_2 = 7 \text{ kg}$

    4. Identify the Answer

    Comparing our result to the given options, the correct mass is 7 kg.

    5. Exam Tip

    In calorimetry problems involving the same substance (like water mixed with water), you can always ignore the specific heat capacity ($c$) because it appears on both sides of the equation and cancels out. This saves you time during the exam! Also, always remember that "boiled water" is a standard code in physics problems for 100°C.

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94. 94.

    If an object sinks in water, it means that

    1. A.Its density is greater than that of water
    2. B.upthrust equals its weight
    3. C.its density is less than that of water
    4. D.water pressure is greater than its weight

    Show answer

    Answer: A. Its density is greater than that of water

    AI explanation

    Analysis of the Question

    This question tests your understanding of Archimedes' Principle and the Law of Flotation. It asks for the physical condition that causes an object to sink when placed in a fluid (in this case, water).

    Concept Explanation

    To determine whether an object will float or sink, we compare two forces acting on it:

    1. Weight ($W$): The downward force due to gravity ($W = mg$).
    2. Upthrust ($U$): The upward force exerted by the fluid on the object.

    According to the Law of Flotation:

    • If Weight > Upthrust, the object sinks.
    • If Weight = Upthrust, the object floats (is in equilibrium).
    • If Weight < Upthrust, the object rises to the surface.

    Since Weight is related to density ($\rho_{object} \times V \times g$) and Upthrust is related to the density of the fluid ($\rho_{fluid} \times V \times g$), the condition for sinking simplifies to the density of the object being greater than the density of the fluid.

    Step-by-Step Solution

    1. Define the variables: Let $\rho_o$ be the density of the object and $\rho_w$ be the density of water.
    2. Analyze the sinking condition: An object sinks when the gravitational force pulling it down is greater than the buoyant force (upthrust) pushing it up.
    3. Relate to density: • Weight of object = $\rho_o \times V \times g$ • Upthrust = $\rho_w \times V \times g$
    4. Compare: For the object to sink, $\rho_o \times V \times g > \rho_w \times V \times g$.
    5. Conclusion: By canceling out the common terms ($V$ and $g$), we find that $\rho_o > \rho_w$. This means the density of the object must be greater than the density of the water.

    Identifying the Answer

    • Option A: Correct. If the object is denser than water, it will sink.
    • Option B: Incorrect. If upthrust equals weight, the object will float in equilibrium.
    • Option C: Incorrect. If the density is less than water, the object will float.
    • Option D: Incorrect. Water pressure acts in all directions and is not the primary factor determining sinking; density is.

    Exam Tip

    Think of it this way: "Denser sinks, lighter floats." If you ever get confused in the exam hall, remember a stone (high density) sinks in water, while a piece of wood (low density) floats. This simple mental model will help you remember the relationship between density and buoyancy every time!

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95. 95.

    Lining the walls of an auditorium with perforated materials reduces

    1. A.reverberation
    2. B.diffraction
    3. C.refraction
    4. D.auditorium pulse

    Show answer

    Answer: A. reverberation

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96. 96.

    A 25cm long pinhole camera produces a one-fifth of an object's size. Calculate the object distance

    1. A.20.49m
    2. B.2.82m
    3. C.4.23m
    4. D.1.25m

    Show answer

    Answer: D. 1.25m

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97. 97.

    A concave mirror of focal length 20cm produces an erect image that is four times the object, the object distance from the mirror is

    1. A.less than 20cm
    2. B.Between 20cm and30cm
    3. C.Between 30cm and 40cm
    4. D.Greater than 40cm

    Show answer

    Answer: A. less than 20cm

    AI explanation

    Analysis

    We are given a concave mirror with a focal length ($f$) of 20 cm. The mirror produces an erect image that is four times the size of the object. We need to find the object distance ($u$).

    Concept

    1. Mirror Formula: $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
    2. Magnification ($m$): $m = \frac{v}{u}$
    3. Sign Convention for Concave Mirrors: • Focal length ($f$) is positive (+20 cm). • For a concave mirror to produce an erect image, the image must be virtual. • Virtual images are formed behind the mirror, so the image distance ($v$) is negative. • Magnification ($m$) for a virtual image is positive.

    Solution

    Step 1: Determine the relationship between $v$ and $u$. Given $m = 4$ and $m = \frac{v}{u}$: $4 = \frac{v}{u} \implies v = 4u$

    Since the image is virtual (erect), we use $v = -4u$ in the mirror formula.

    Step 2: Apply the mirror formula. $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ $\frac{1}{20} = \frac{1}{u} + \frac{1}{-4u}$

    Step 3: Solve for $u$. Find a common denominator for the right side ($4u$): $\frac{1}{20} = \frac{4 - 1}{4u}$ $\frac{1}{20} = \frac{3}{4u}$

    Cross-multiply: $4u = 60$ $u = \frac{60}{4}$ $u = 15 \text{ cm}$

    Step 4: Compare with the options. We found the object distance to be 15 cm. Since 15 cm is less than the focal length of 20 cm, it falls into the category of "less than 20 cm."

    Conclusion

    The object must be placed between the pole and the principal focus of the concave mirror to produce an erect, magnified, virtual image. Since 15 cm < 20 cm, the correct option is A.

    Exam Tip

    For any concave mirror, remember this rule: if the object is placed at or beyond the focal point, the image is always real and inverted. The only way to get an erect (virtual) image with a concave mirror is to place the object between the pole and the focal point ($u < f$). Since your focal length is 20 cm, any answer that isn't less than 20 cm is physically impossible for an erect image!

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98. 98.

    Copper of 0.2g and silver of 1.2g are deposited when current is passed through copper and silver voltameter. Calculate the electrochemical equivalent, Z of silver if that of copper is 0.00028gC$^{-1}$

    1. A.1.68 x 10$^{-3}$gC$^{-1}$
    2. B.2.34 x 10$^{-3}$gC$^{-1}$
    3. C.2.80 x 10$^{-3}$gC$^{-1}$
    4. D.3.34 x 10$^{-3}$gC$^{-1}$

    Show answer

    Answer: A. 1.68 x 10$^{-3}$gC$^{-1}$

    AI explanation

    Analysis

    This question is based on Faraday’s Laws of Electrolysis. Specifically, it deals with the relationship between the mass of a substance deposited during electrolysis and its electrochemical equivalent (Z).

    Concept

    According to Faraday’s second law of electrolysis, when the same quantity of electricity ($Q$) is passed through different electrolytes connected in series, the mass ($m$) of the substance deposited is directly proportional to its electrochemical equivalent ($Z$).

    The formula is:

    $\frac{m_1}{Z_1} = \frac{m_2}{Z_2} = Q$

    Where:

    • $m_1$ = mass of copper = $0.2\text{ g}$
    • $Z_1$ = electrochemical equivalent of copper = $0.00028\text{ gC}^{-1}$
    • $m_2$ = mass of silver = $1.2\text{ g}$
    • $Z_2$ = electrochemical equivalent of silver = ?

    Solution

    1. Set up the equation: $$\frac{m_{copper}}{Z_{copper}} = \frac{m_{silver}}{Z_{silver}}$$

    2. Substitute the known values: $$\frac{0.2}{0.00028} = \frac{1.2}{Z_{silver}}$$

    3. Cross-multiply to solve for $Z_{silver}$: $$0.2 \times Z_{silver} = 1.2 \times 0.00028$$ $$0.2 \times Z_{silver} = 0.000336$$

    4. Divide by 0.2: $$Z_{silver} = \frac{0.000336}{0.2}$$ $$Z_{silver} = 0.00168\text{ gC}^{-1}$$

    5. Convert to standard form: $$0.00168 = 1.68 \times 10^{-3}\text{ gC}^{-1}$$

    Conclusion

    Comparing our result with the given options, we find that it matches option A.

    Exam Tip

    When dealing with electrolysis problems in JAMB, always check if the substances are in series. If they are, the charge ($Q = It$) is the same for both. If you ever forget the formula, remember that mass is directly proportional to the electrochemical equivalent; just set up a simple ratio!

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99. 99.

    The speed of sound in air is 60 m/s. How far from the centre of a storm is an observer who hears a thunder clap 4s after the flash of the lightning?

    1. A.140m
    2. B.100m
    3. C.340m
    4. D.240m

    Show answer

    Answer: D. 240m

    AI explanation

    1. Analyze the question

    We are given the speed of sound ($v$) and the time interval ($t$) between seeing the lightning flash and hearing the thunder. We need to calculate the distance ($d$) from the observer to the source of the storm.

    2. Explain the concept

    In physics, the relationship between distance, speed, and time is defined by the formula:

    $\text{Distance} = \text{Speed} \times \text{Time}$

    Since light travels almost instantaneously compared to sound, the time delay between the flash and the sound is effectively the time it takes for the sound wave to travel from the storm to the observer.

    3. Show the solution

    • Given: • Speed of sound ($v$) = $60 \text{ m/s}$ • Time ($t$) = $4 \text{ s}$

    • Calculation: • $d = v \times t$ • $d = 60 \text{ m/s} \times 4 \text{ s}$ • $d = 240 \text{ m}$

    4. Identify the answer

    Based on the calculation, the distance is 240 meters. This corresponds to option D.

    (Note: In real-world physics, the speed of sound in air is typically around 330–340 m/s. However, for the purpose of this specific JAMB question, we must use the value provided in the prompt, which is 60 m/s.)

    5. Tip

    When solving speed-distance-time problems, always check your units. If the speed is in m/s and the time is in seconds, your distance will automatically be in meters. If the time were given in minutes, you would need to convert it to seconds first!

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100. 100.

     The thermometric property of mercury is best on the change in

     1. A.density with temperature
     2. B.volume with temperature
     3. C.pressure with temperature
     4. D.resistance with temperature

     Show answer

     Answer: B. volume with temperature

     AI explanation

     Analysis

     The question asks for the specific physical property of mercury that allows it to function as a thermometric substance in a liquid-in-glass thermometer.

     Concept Explanation

     A thermometric property is any physical property of a substance that changes linearly and predictably with temperature. For a liquid-in-glass thermometer (like the one containing mercury), the thermometer works because the liquid expands when heated and contracts when cooled.

     • Volume expansion: As the temperature of the mercury increases, the kinetic energy of its atoms increases, causing them to move further apart. This results in a measurable increase in the volume of the mercury, which causes the liquid level to rise in the narrow capillary tube of the thermometer.
     • Why others are incorrect: While density does change with temperature (as volume increases, density decreases), the direct observable change that indicates the temperature on the scale is the change in volume. Pressure is the primary thermometric property for gas thermometers, and resistance is the thermometric property for platinum resistance thermometers.

     Step-by-Step Solution

     1. Identify the device: The question refers to a mercury thermometer.
     2. Observe the mechanism: In a mercury thermometer, we observe the mercury column rising or falling in a glass tube.
     3. Relate to physics: The rise or fall of the column is a direct consequence of the mercury expanding or contracting. Expansion and contraction are changes in the volume of the substance.
     4. Conclusion: Since the mercury occupies more space (volume) as it gets hotter, the change in volume is the property used to calibrate the temperature scale.

     Final Answer

     The correct option is B.

     Exam Tip: Always remember the "thermometric property" rule:

     • Liquid-in-glass thermometers (Mercury/Alcohol) $\rightarrow$ Volume
     • Resistance thermometers $\rightarrow$ Electrical Resistance
     • Constant volume gas thermometers $\rightarrow$ Pressure
     • Thermocouples $\rightarrow$ Electromotive Force (e.m.f)

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101. 101.

     The power of a lens in diopters is

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

     Show answer

     Answer: B. $\frac{1}{\text{f}}$

     AI explanation

     Analysis

     The question asks for the mathematical definition of the power of a lens, specifically when measured in diopters.

     Concept

     In optics, the power of a lens ($P$) is a measure of its ability to converge or diverge light rays. It is defined as the reciprocal of the focal length ($f$) of the lens, provided that the focal length is measured in meters.

     The unit of power is the diopter (D), where $1 \text{ diopter} = 1 \text{ m}^{-1}$.

     The formula is expressed as:

     $P = \frac{1}{f(\text{in meters})}$

     Solution

     1. Identify the relationship: The power of a lens is inversely proportional to its focal length.
     2. Apply the unit constraint: For the power to be expressed in diopters, the focal length $f$ must be in meters.
     3. Formulate the equation: $P = \frac{1}{f}$.
     4. Compare with the given options: • Option A: $3f$ (Incorrect) • Option B: $\frac{1}{f}$ (Correct) • Option C: $2f$ (Incorrect) • Option D: $f$ (Incorrect)

     Exam Tip

     Always check the units! If a JAMB question gives you the focal length in centimeters (cm), you must convert it to meters (m) by dividing by 100 before using the formula $P = \frac{1}{f}$. For example, if $f = 20\text{ cm}$, convert it to $0.2\text{ m}$, then $P = \frac{1}{0.2} = 5\text{ diopters}$.

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

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