2020 WAEC (WASSCE) Physics Past Questions and Answers

Questions

1. 1.

   The magnitude of the force experienced by a charge of 1.6 x 10$^{-8}$C in a uniform electric field of intensity 5 x 10$^5$NC$^{-1}$  is

   1. A.3.2 x 10$^{-14}$N
   2. B.8.0 x 10$^{-13}$N
   3. C.8.0 x 10$^{-3}$N
   4. D.3.1 x 10$^{13}$ N

   Show answer

   Answer: C. 8.0 x 10$^{-3}$N

   AI explanation

   Analyze the question: We're given a charge q = 1.6 × 10⁻⁸ C placed in a uniform electric field of intensity E = 5 × 10⁵ N/C. We need the force on the charge.

   Concept: Electric field intensity is the force per unit charge:

   E = F/q, so F = qE

   Solution:

   F = (1.6 × 10⁻⁸ C) × (5 × 10⁵ N/C)

   F = (1.6 × 5) × 10⁻⁸⁺⁵

   F = 8.0 × 10⁻³ N

   Check against the options:

   • A (3.2 × 10⁻¹⁴ N): wrong, this is far too small.
   • B (8.0 × 10⁻¹³ N): wrong, the powers of 10 were not combined correctly.
   • C (8.0 × 10⁻³ N): matches our result.
   • D (3.1 × 10¹³ N): wrong, this comes from dividing (5 × 10⁵ ÷ 1.6 × 10⁻⁸ ≈ 3.1 × 10¹³) instead of multiplying.

   Tip: Remember the triangle F = qE. Force is multiplied by charge and field. When multiplying powers of ten, add the exponents: −8 + 5 = −3. Option D is a trap for students who divide instead of multiply, so always check which operation the formula needs.

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2. 2.

   An electrical device has 50 turns in its primary coil  and 20 turns in the secondary coil. The device can be a\an?

   1. A.step-up transformer
   2. B.step-down transformer
   3. C.d.c generator
   4. D.a.c generator

   Show answer

   Answer: B. step-down transformer

   AI explanation

   Analyze the question: The device has a primary coil (50 turns) and a secondary coil (20 turns). Having a primary and a secondary coil is the signature of a transformer, so we need to decide whether it steps voltage up or down.

   Concept: For an ideal transformer:

   Vs / Vp = Ns / Np

   • If Ns > Np, the output voltage is larger than the input, so it is a step-up transformer.
   • If Ns < Np, the output voltage is smaller than the input, so it is a step-down transformer.

   Solution:

   • Np = 50 turns
   • Ns = 20 turns

   Ns / Np = 20 / 50 = 0.4

   Since the ratio is less than 1 (Ns < Np), the secondary voltage is only 0.4 times the primary voltage. For example, a 250 V input would give 100 V at the output. The voltage is reduced, so the device is a step-down transformer.

   Why not the others?

   • A (step-up): this would need more turns in the secondary than in the primary.
   • C and D (d.c. and a.c. generators): generators have a single armature coil rotating in a magnetic field. They do not have "primary" and "secondary" coils.

   Answer: B, step-down transformer.

   Exam tip: Compare the turns. Secondary fewer than primary means step-down, and secondary more than primary means step-up. A memory trick is "Secondary Smaller = Step-down."

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3. 3.

   An image formed on a screen is always?

   1. A.inverted
   2. B.magnified
   3. C.upright
   4. D.virtual

   Show answer

   Answer: A. inverted

   AI explanation

   Analyze the question The question asks about an image formed on a screen. In optics, the key idea is whether the image is real or virtual.

   Explain the concept

   • A real image is formed when light rays actually meet at a point. It can be captured on a screen.
   • A virtual image is formed when light rays only appear to come from a point (they diverge). It cannot be captured on a screen.

   Work through the options

   • D. Virtual: Wrong. Virtual images cannot be projected onto a screen.
   • C. Upright: Wrong. Real images formed by a single lens or mirror are normally inverted, not upright.
   • B. Magnified: Wrong. Real images can be magnified, the same size, or diminished, depending on the object's position. A camera, for example, forms a diminished image.
   • A. Inverted: This is the best answer. An image formed on a screen is real, and real images formed by a single converging lens or concave mirror are inverted relative to the object.

   Note: The strictly correct statement is that an image on a screen is real. Since "real" is not an option, "inverted" is the best choice.

   Tip: Remember "Real = Rays meet = Screen = Reversed (inverted)". Virtual images are upright and cannot be put on a screen.

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4. 4.

   A diver steps off a diving platform that is 10m above the water. If there is no air resistance during the fall, there will be a decrease in the diver's

   1. A.gravitational potential energy
   2. B.total mechanical energy
   3. C.kinetic energy
   4. D.momentum

   Show answer

   Answer: A. gravitational potential energy

   AI explanation

   Analyze the question: A diver falls freely from 10 m with no air resistance. Which quantity decreases during the fall?

   Concept: In free fall without air resistance, only gravity does work, so mechanical energy is conserved:

   • Gravitational potential energy (PE = mgh) depends on height. As the diver falls, h decreases, so PE decreases.
   • Kinetic energy (KE = ½mv²) depends on speed. As the diver speeds up (v = gt), KE increases.
   • Total mechanical energy (PE + KE) stays constant, since there is no air resistance to remove energy.
   • Momentum (p = mv) increases because the velocity increases.

   Step-by-step check of each option:

   • A. Gravitational potential energy: decreases as the diver loses height (from mg(10) toward 0). ✔
   • B. Total mechanical energy: constant, because energy is conserved. ✘
   • C. Kinetic energy: increases. ✘
   • D. Momentum: increases. ✘

   Answer: The only quantity that decreases is the diver's gravitational potential energy.

   Tip: In free fall (no air resistance), remember "PE goes down, KE goes up, total stays the same." When a question asks what decreases, look for the quantity tied to height. If air resistance were present, total mechanical energy would also decrease because some of it would be lost as heat.

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5. 5.

   The quantity of motion of a body is its

   1. A.acceleration
   2. B.displacement
   3. C.mometum
   4. D.velocity

   Show answer

   Answer: C. mometum

   AI explanation

   1. Analyze the question "Quantity of motion" is the classical name for a physical quantity that combines how much matter a body has with how fast it moves.

   2. Explain the concept Isaac Newton described momentum as the "quantity of motion" of a body. It depends on two things:

   • the mass of the body (m)
   • the velocity of the body (v)

   Momentum (p) = mass × velocity = mv

   • SI unit: kg m/s (or N s)
   • It is a vector quantity, so it has both magnitude and direction.

   3. Check each option

   • A. Acceleration: This is the rate of change of velocity (a = Δv/t). It does not involve mass, so it is not the quantity of motion.
   • B. Displacement: This is the distance moved in a particular direction. It describes position change, not the quantity of motion.
   • C. Momentum: This is mass × velocity, which is exactly the "quantity of motion."
   • D. Velocity: This is the rate of change of displacement. It has no mass component, so it is only part of what makes up momentum.

   4. Answer The correct option is C. momentum (spelled "mometum" in the question, which is just a typo).

   5. Exam tip Link the phrases to the quantities:

   • "Quantity of motion" → momentum (mv)
   • "Rate of change of momentum" → force
   • "Rate of change of velocity" → acceleration

   If you see "quantity of motion," think of mass and velocity together. Keep going, you're doing well!

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6. 6.

   Which of the following machines does not apply the lever principle?

   1. A.Claw hammer
   2. B.Wheelbarrow
   3. C.Single pulley
   4. D.sugar tong

   Show answer

   Answer: C. Single pulley

   AI explanation

   Analyze the question: We need the machine that does not work on the lever principle (a rigid bar turning about a fixed pivot/fulcrum, with effort and load applied at different points).

   Explain the concept: A lever has three parts: the fulcrum, the effort, and the load. Levers come in three classes:

   • First class: fulcrum between effort and load (e.g. scissors, seesaw)
   • Second class: load between fulcrum and effort (e.g. wheelbarrow, nut cracker)
   • Third class: effort between fulcrum and load (e.g. sugar tongs, forceps, fishing rod)

   Solution, option by option:

   • A. Claw hammer: When pulling out a nail, the hammer pivots on its head. This is a lever (first class).
   • B. Wheelbarrow: The wheel is the fulcrum, the load is in the middle, and the effort is at the handles. This is a second-class lever.
   • C. Single pulley: A fixed single pulley is a wheel with a rope running over it. It only changes the direction of the effort and gives a mechanical advantage of 1. It is classed as a pulley system, not a lever, in the usual WASSCE treatment. (Strictly, a pulley can be modelled as a lever with equal arms, but it is not one of the standard "lever" machines.)
   • D. Sugar tong: Two arms are joined at one end (the fulcrum), with the effort in the middle and the load at the other end. This is a third-class lever.

   Answer: The single pulley is the one that does not apply the lever principle, so the answer is C.

   Tip: For "which is not a lever" questions, look for a pivoting bar. Pulleys, inclined planes, screws, and gears are different simple machines, while hammers, barrows, tongs, scissors, and pliers are levers.

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7. 7.

   The velocity of sound in air at 15°C is 340ms$^{-1}$. Calculate the velocity at 47$^o$C

   1. A.790ms$^{-1}$
   2. B.602ms$^{-1}$
   3. C.358ms$^{-1}$
   4. D.322ms$^{-1}$

   Show answer

   Answer: C. 358ms$^{-1}$

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8. 8.

   A ray of light travels obliquely from a less dense medium to a denser medium. Which of the following statements is true about the light?

   1. A.The wavelength of the light increases in the second medium
   2. B.The speed of the light increases in the second medium
   3. C.The light refracts towards the normal
   4. D.There Is a change in the frequency of the light

   Show answer

   Answer: C. The light refracts towards the normal

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9. 9.

   An a.c. generator can be converted to a d.c. electric motor by replacing the

   1. A.slip rings with a split ring and connecting a battery
   2. B.split ring with slip rings and connecting a battery
   3. C.a.c. with d.c. source and connecting slip rings
   4. D.a.c. with d.c. source and connecting split rings

   Show answer

   Answer: A. slip rings with a split ring and connecting a battery

   AI explanation

   Analyze the question: We are asked how to convert an a.c. generator into a d.c. motor. We need to compare the parts of the two machines.

   Concept:

   • An a.c. generator (alternator) has slip rings. They carry the alternating current from the rotating coil to the external circuit without reversing it.
   • A d.c. motor has a split-ring commutator. It reverses the current in the coil every half turn, so the torque always acts in the same direction and the coil keeps rotating one way.
   • A motor needs an electrical input. A generator needs a mechanical input (turning the coil) and gives out electrical energy.

   Step-by-step solution:

   1. The a.c. generator's slip rings would make the force on the coil's sides reverse every half turn. The coil would just oscillate and not rotate continuously. So the slip rings must be replaced.
   2. Replace the slip rings with a split ring (commutator). This keeps the torque in one direction.
   3. Connect a battery (d.c. source) to supply current to the coil through the brushes. The coil then sits in the magnetic field and experiences a force (motor effect, Fleming's left-hand rule).

   Checking the options:

   • A. Slip rings replaced with a split ring and a battery connected. This is correct.
   • B. This is the reverse. It would turn a motor into a generator, not the other way round.
   • C and D. These are badly worded. You cannot replace "a.c." with "d.c." as a component, and C keeps the slip rings, which would not give continuous rotation.

   Answer: A

   Tip: Remember "Slip rings → a.c. generator; Split ring → d.c. motor." For a motor, think "split ring + battery in". For a generator, think "turn the coil to get current out".

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10. 10.

    A beam consisting of $\alpha$-particles. $\beta$-particles and $\gamma$-rays pass through a magnetic field at right angles to the direction of the field. Which of the following observations would be made about the $\alpha$-particles, $\beta$-particles, and $\gamma$-rays respectively?

    1. A.Deflected, deflected, deflected
    2. B.Deflected, deflected, not deflected
    3. C.Deflected, not deflected, deflected
    4. D.Not deflected, deflected, deflected

    Show answer

    Answer: B. Deflected, deflected, not deflected

    AI explanation

    Analyze the question: The beam has three kinds of radiation moving at right angles to a magnetic field. We need to decide which are deflected.

    Concept: A magnetic field exerts a force only on moving charged particles. The force is

    F = qvB sin θ

    When the motion is perpendicular to the field (θ = 90°), sin θ = 1, so F = qvB. If q = 0, then F = 0 and there is no deflection.

    Solution:

    • α-particles are helium nuclei with charge +2e. They are charged, so they are deflected.
    • β-particles are fast electrons (or positrons) with charge −e (or +e). They are charged, so they are deflected. They bend in the opposite direction to the α-particles, and more sharply because they are much lighter.
    • γ-rays are electromagnetic waves (photons) with no charge. They are not deflected.

    So the order is: deflected, deflected, not deflected.

    **Answer: B.

    Tip: Remember "charge = deflection". Alpha and beta carry charge, so they bend in electric and magnetic fields. Gamma has no charge, so it goes straight. Use Fleming's left-hand rule to find the direction of deflection for the charged ones.

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11. 11.

    A moving-coil galvanometer which gives a full-scale on deflection with 0.005A is converted to a voltmeter reading up to 5V using an external resistance of 975$\Omega$. What is the resistance of the metre?

    1. A.0.25$\Omega$
    2. B.2.50$\Omega$
    3. C.25.00$\Omega$
    4. D.250.00$\Omega$

    Show answer

    Answer: C. 25.00$\Omega$

    AI explanation

    Analyze the question: A galvanometer is converted to a voltmeter by connecting a high resistance (multiplier) in series with it. We need the galvanometer's own resistance (the "meter" resistance).

    Concept: For a voltmeter made this way, the full-scale voltage V is shared across the series combination:

    V = Ig(G + R)

    where

    • Ig = full-scale current = 0.005 A
    • R = external series resistance = 975 Ω
    • G = galvanometer resistance (unknown)
    • V = 5 V

    Solution:

    Total resistance needed: G + R = V / Ig = 5 / 0.005 = 1000 Ω

    So: G = 1000 − 975 = 25 Ω

    Check: Total resistance = 25 + 975 = 1000 Ω, and current = 5/1000 = 0.005 A, which matches full-scale deflection.

    Answer: The resistance of the meter is 25.00 Ω, which is option C.

    Tip: For converting a galvanometer to a voltmeter, always think "series": find the total resistance with V/Ig, then subtract the known resistance. For an ammeter, the shunt is in parallel instead.

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

13. 13.

    Which of the following statement about viscosity is not true? it

    1. A.depends on areas of the surfaces in contact
    2. B.occurs in fluids
    3. C.is independent of the relative velocity of the layers
    4. D.depends on the tangential force between the layers

    Show answer

    Answer: C. is independent of the relative velocity of the layers

    AI explanation

    Analyze the question: We need the statement about viscosity that is NOT true.

    Concept: Viscosity is the internal friction in a fluid (liquid or gas) that opposes relative motion between adjacent layers. Newton's law of viscosity gives:

    F = ηA(dv/dx)

    where

    • F = tangential (viscous) force between the layers
    • η = coefficient of viscosity
    • A = area of the layers in contact
    • dv/dx = velocity gradient (change in relative velocity between layers over their separation)

    Check each option:

    • A. Depends on areas of the surfaces in contact: True. From F = ηA(dv/dx), the viscous force is proportional to the area A.
    • B. Occurs in fluids: True. Viscosity is a property of liquids and gases.
    • C. Is independent of the relative velocity of the layers: Not true. The viscous force is directly proportional to the velocity gradient, so it depends on the relative velocity of the layers. (Only the coefficient η is independent of velocity for Newtonian fluids, but the viscous force itself is not.)
    • D. Depends on the tangential force between the layers: True. The viscous force is tangential to the layers, and it is what F represents in the formula.

    Tip: In "which is NOT true" questions, test each option against the formula. Here F = ηA(dv/dx) contains area, force, and velocity gradient, so any statement denying one of these dependencies is the likely false one.

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14. 14.

    Two identical cups containing the same volume of water at 45°C and 5°C, are left in a room at 25°C. Which of the following graphs correctly illustrates the variation of temperature with time?

    

    1. A.A
    2. B.B
    3. C.C
    4. D.D

    Show answer

    Answer: A. A

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15. 15.

    An electron of mass m and charge e moves in a circular path in a magnetic field of flux density B. How long does it take to complete one orbit?

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

    Show answer

    Answer: C. $\frac{2\pi m}{Be}$

    AI explanation

    Analyze the question: A charged particle moves in a circle because the magnetic force acts as the centripetal force. We need the time for one complete orbit, which is the period T.

    Concept: The magnetic force on a charge moving perpendicular to a field is F = Bev. The centripetal force needed for circular motion is F = mv²/r.

    Solution:

    1. Equate the two forces: Bev = mv²/r

    2. Solve for the radius: r = mv/(Be)

    3. The period is the circumference divided by the speed: T = 2πr/v

    4. Substitute r: T = 2π(mv/(Be))/v = 2πm/(Be)

    The speed v cancels, so the period does not depend on how fast the electron moves or on the size of the orbit.

    Checking the options:

    • A and B have the wrong variables in the wrong places (B or m and e in the same part of the fraction), so they don't match.
    • D, Be/(2πm), is the frequency (f = 1/T), not the period.
    • C, 2πm/(Be), matches our result.

    Tip: Remember that T = 2πm/(Be) is the period and f = Be/(2πm) is the frequency. Period is "time", so the mass (m) sits on top. If an option looks like the inverse, it is the frequency, a common trap in WASSCE and JAMB questions.

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16. 16.

    The material used to slow down the neutrons in a nuclear reactor is

    1. A.boron
    2. B.copper
    3. C.graphite
    4. D.uranium

    Show answer

    Answer: C. graphite

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17. 17.

    How would the capacitance of a parallel plate capacitor be affected if the distance of separation of its plates is decreased? It will

    1. A.increase in value
    2. B.decrease slightly
    3. C.remain unchanged
    4. D.drop to zero

    Show answer

    Answer: A. increase in value

    AI explanation

    Analyze the question: We want to know what happens to the capacitance (C) of a parallel plate capacitor when the plate separation (d) is decreased.

    Concept: The capacitance of a parallel plate capacitor is given by:

    C = ε₀εᵣA / d

    where

    • ε₀ = permittivity of free space
    • εᵣ = relative permittivity of the material between the plates
    • A = area of overlap of the plates
    • d = distance between the plates

    Solution:

    1. From the formula, C is inversely proportional to d (C ∝ 1/d), provided A and the dielectric stay the same.
    2. If d decreases, the denominator becomes smaller, so the value of C becomes larger.
    3. Example: if d is halved, C doubles.

    Physical reason: when the plates are closer, the electric field from one plate is more effective at attracting opposite charge on the other plate. The capacitor can therefore store more charge for the same potential difference, and since C = Q/V, the capacitance rises.

    Checking the options:

    • A. Increase in value ✔ (matches C ∝ 1/d)
    • B. Decrease slightly ✘ (opposite of the true effect)
    • C. Remain unchanged ✘ (d is in the formula, so C changes)
    • D. Drop to zero ✘ (C would only approach zero if d became very large)

    Exam tip: Remember "Area Aids, Distance Dims", meaning capacitance goes up with larger Area and down with larger Distance. So decreasing the distance increases capacitance. Also, inserting a dielectric with a higher εᵣ increases C too.

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18. 18.

    Which of the following statements about the process of melting of a solid are true? The temperature of the solid will  I. remain steady until melting starts. ll. keep rising until melting starts, Ill remain steady as melting proceeds.  V, keep rising as melting proceeds.

    1. A.I and llI only
    2. B.IlI and IV only
    3. C.I, Il and Ill only
    4. D.ll and IV only

    Show answer

    Answer: A. I and llI only

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19. 19.

    Which of the following statements correctly explains why a total solar eclipse would be seen by people on only a small portion of the earth's surface? The

    1. A.moon is larger in diameter than the earth
    2. B.eath is larger in diameter than the sun
    3. C.earth revolves around the sun
    4. D.earth is larger in diameter than the moon.

    Show answer

    Answer: D. earth is larger in diameter than the moon.

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20. 20.

    The length of an iron bar is 100cm at 20°C. At what temperature will its length increase by 0.01%? [Linear expansivity of iron = 1.2 x 10$^{-5}$°C]

    1. A.48.0°C
    2. B.38.0°C
    3. C.28.3°C
    4. D.23.0°C

    Show answer

    Answer: C. 28.3°C

    AI explanation

    Analyze the question: An iron bar of length 100 cm at 20°C expands by 0.01% of its original length. We need the temperature at which this happens, given α = 1.2 × 10⁻⁵ °C⁻¹.

    Concept: Linear expansion is given by

    ΔL = L₀ α Δθ, so Δθ = ΔL / (L₀ α)

    Solution:

    1. Increase in length: 0.01% of 100 cm = (0.01/100) × 100 = 0.01 cm
    2. Substitute: Δθ = 0.01 / (100 × 1.2 × 10⁻⁵) Δθ = 0.01 / (1.2 × 10⁻³) Δθ ≈ 8.33°C
    3. Final temperature = 20 + 8.33 = 28.33°C ≈ 28.3°C

    Tip: For percentage expansion questions, you can skip the length entirely. A fractional increase of 0.01% = 1 × 10⁻⁴, so Δθ = (1 × 10⁻⁴) / α = (1 × 10⁻⁴)/(1.2 × 10⁻⁵) = 8.33°C. Don't forget to add the starting temperature (20°C) because the question asks for the final temperature, not the change in temperature. Options like D (23.0°C) are traps for students who forget to finish the calculation.

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21. 21.

    Which of the following waves requires a material medium for its propagation?

    1. A.Radio waves
    2. B.Light waves
    3. C.Sound waves
    4. D.X-rays

    Show answer

    Answer: C. Sound waves

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22. 22.

    In the hydraulic press, the force F applied is related to the diameter d of the cylinder by

    1. A.F $\alpha$ d$^2$
    2. B.F $\alpha$ d
    3. C.F $\alpha$ d$^{-1}$
    4. D.F $\alpha$ d$^{-2}$

    Show answer

    Answer: A. F $\alpha$ d$^2$

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23. 23.

    A 60kg man stands on a weighing balance in an elevator. If the elevator accelerates upwards at 5ms$^{-2}$, determine the reading of the scale. [g = 10ms$^{-2}$]

    1. A.300N
    2. B.600N
    3. C.800N
    4. D.900N

    Show answer

    Answer: D. 900N

    AI explanation

    Analyze the question: A man stands on a scale in a lift accelerating upwards. The scale reads the normal reaction force R, which is the force the scale exerts on the man.

    Concept: When a lift accelerates upwards, the scale must push up with more force than the man's weight, so he feels "heavier". Apply Newton's second law:

    R − mg = ma, so R = m(g + a)

    Solution:

    • Mass, m = 60 kg
    • g = 10 m/s²
    • a = 5 m/s² (upwards)

    Weight = mg = 60 × 10 = 600 N

    Net force needed = ma = 60 × 5 = 300 N

    R = mg + ma = 600 + 300 = 900 N

    Answer: D. 900N

    Tip: Remember the pattern for lift problems:

    • Accelerating up (or decelerating while moving down): R = m(g + a), so the reading is larger.
    • Accelerating down (or decelerating while moving up): R = m(g − a), so the reading is smaller.
    • Constant velocity or at rest: R = mg.

    Option B (600 N) is the trap for students who forget the lift's acceleration, and option A (300 N) is just ma on its own.

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24. 24.

    The volume of a fixed mass of a gas varies inversely as the pressure on it provided the temperature is constant. This statement is

    1. A.Pressure law
    2. B.Charles law
    3. C.Boyle's law
    4. D.General gas law

    Show answer

    Answer: C. Boyle's law

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25. 25.

    A motorcycle starting from rest is uniformly accelerated such that its velocity in 10s is 72kmhr$^{-1}$. What is its acceleration?

    1. A.108ms$^2$
    2. B.86ms$^2$
    3. C.4ms$^2$
    4. D.2ms$^2$

    Show answer

    Answer: D. 2ms$^2$

    AI explanation

    Analyze the question: The motorcycle starts from rest (u = 0), reaches a velocity v = 72 km/h in t = 10 s. We need the acceleration a. Concept: For uniform acceleration, a = (v − u) / t Units must be consistent, so convert km/h to m/s first. Conversion: 72 km/h = 72 × 1000 m / 3600 s = 72 × (5/18) = 20 m/s Solution: a = (20 − 0) / 10 = 2 m/s² Check the options: The options are written as "ms²", but they clearly mean m/s² (ms⁻²). Answer: D (2 m/s²) Tip: To convert km/h to m/s, multiply by 5/18. Many students lose marks by plugging 72 straight into the formula. If you did that, you would get 7.2, which is not an option, a sign that something is wrong. Also, 72 is a handy number because 72 × 5/18 = 20 exactly. Always convert units before substituting.

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26. 26.

    Which of the following statements explain why hot soapy water is more effective in cleaning oil-stained dishes?

    1. A.The oil on the dishes repels the soap
    2. B.soap and heat decrease the surface tension of oil
    3. C.soap increases the surface tension of oil and water
    4. D.Hot water increases the surface tension of oil

    Show answer

    Answer: B. soap and heat decrease the surface tension of oil

    AI explanation

    Step 1: Analyze the question We need to know why hot, soapy water cleans greasy dishes better than plain cold water. This is about surface tension.

    Step 2: The concept

    • Surface tension is the tendency of a liquid surface to contract, caused by cohesive forces between molecules.
    • Soap is a surfactant (detergent). It lowers the surface tension of water, so the water can spread, wet the surface and mix with the oil. The soap molecules have a water-loving head and an oil-loving tail, so they surround oil droplets and lift them off the dish (emulsification).
    • Heating a liquid weakens the cohesive forces between its molecules, so surface tension decreases as temperature rises. Heat also lowers the viscosity of the oil, so it flows and dislodges more easily.

    Step 3: Check each option

    • A. Wrong. The oil does not repel soap. Soap molecules actually attach to oil with their tails.
    • B. Correct. Soap and heat both decrease surface tension, which helps the water spread, penetrate and break up the oil.
    • C. Wrong. Soap decreases surface tension and does not increase it.
    • D. Wrong. Heat decreases surface tension and does not increase it.

    Step 4: Answer Strictly speaking, soap mainly lowers the surface tension of the water, and the oil is emulsified, but B is the only option that is physically correct in its overall idea.

    Tip: Remember "Soap and heat reduce surface tension." Whenever you see temperature or detergent in a surface tension question, think of the tension going down. Any option saying "increases" is almost always a distractor.

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27. 27.

    When two cells of negligible internal resistances and equal e.m.f. denoted by E$_1$ and E$_2$ are connected in parallel, combined e.m.f. E is given by

    1. A.E = E$_1$ + E$_2$
    2. B.$\frac{1}{E} = \frac{1}{E_1} + \frac{1}{E_2}$
    3. C.E = E$_1$ = E$_2$
    4. D.E = $\frac{E_1}{E_2}$

    Show answer

    Answer: C. E = E$_1$ = E$_2$

    AI explanation

    Analyze the question: Two cells with negligible internal resistance and equal e.m.f. (E₁ = E₂) are connected in parallel. We need the combined e.m.f.

    Concept:

    • Cells in series (aiding): e.m.f.s add, so E = E₁ + E₂.
    • Cells in parallel: the combined e.m.f. is the same as that of a single cell, provided the cells have equal e.m.f. The cells share the current, but the potential difference across the combination does not increase.

    Solution:

    1. Connecting the cells in parallel means their positive terminals are joined together and their negative terminals are joined together.
    2. The potential difference between the common terminals is fixed by the e.m.f. of one cell, since the other has the same e.m.f.
    3. Because the e.m.f.s are equal and the internal resistances are negligible, no current circulates between the cells, and the terminal p.d. is just E₁, which equals E₂.

    So:

    E = E₁ = E₂

    Checking the other options:

    • A: E₁ + E₂ applies to cells in series, not parallel.
    • B: This has the form used for resistors or capacitors in certain arrangements, and it is not a rule for e.m.f.
    • D: A ratio of e.m.f.s has no physical meaning here.

    **Correct answer: C.

    Tip: Parallel cells give the same voltage but a longer-lasting supply, because the current is shared. Series cells give a higher voltage. Remember it as "Series adds voltage, parallel adds lifespan."

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28. 28.

    Which of the current-voltage characteristics shown above is that exhibited an ohmic conductor?

    1. A.A
    2. B.B
    3. C.C
    4. D.D

    Show answer

    Answer: A. A

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29. 29.

    The diagram illustrates a ball of mass m sliding down a plank inclined at an angle of 0 to the horizontal. The kinetic friction between the ball and the plank is F, and the acceleration of free fall is g. The normal force on the ball is?

    1. A.mgsin $\theta$
    2. B.mgtan $\theta$, mgcos $\theta$
    3. C.mgcos $\theta$
    4. D.mgcot $\theta$

    Show answer

    Answer: C. mgcos $\theta$

    AI explanation

    Analyze the question

    A ball of mass m slides down a plank inclined at angle θ to the horizontal. We need the normal force exerted by the plank on the ball.

    Concept

    The normal force acts perpendicular to the surface. The ball does not move perpendicular to the plank, so the forces in that direction must balance. The weight mg splits into two components:

    • Parallel to the plank (down the slope): mg sin θ
    • Perpendicular to the plank (into the surface): mg cos θ

    Solution

    Perpendicular to the plank, there is no acceleration, so:

    N − mg cos θ = 0 N = mg cos θ

    The kinetic friction F acts along the plank, up the slope. It does not affect the normal force. It only enters the equation along the slope: mg sin θ − F = ma.

    Checking the options

    • A. mg sin θ is the component of weight along the slope, not the normal force.
    • B. The option is garbled. It lists mg tan θ and also mg cos θ, but mg tan θ is not correct. Only mg cos θ would be right here, and option C states that cleanly.
    • C. mg cos θ is correct.
    • D. mg cot θ has no physical basis here.

    Tip

    On an incline, remember "cos is for the contact": the normal force is mg cos θ, and the force along the slope is mg sin θ. Check the limits. At θ = 0 (flat surface), N should equal mg, and cos 0 = 1, so it works. Friction never changes the normal force on a slope with no extra vertical forces.

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30. 30.

    In collision between two objects, kinetic energy is conserved only if

    1. A.one of the objects was initially at rest
    2. B.potential energy is converted to work
    3. C.the collision is inelastic
    4. D.the collision is elastic

    Show answer

    Answer: D. the collision is elastic

    AI explanation

    Analyze the question: We're asked under what condition kinetic energy is conserved in a collision between two objects.

    Concept: Collisions fall into two main types:

    • Elastic collision: Both momentum and kinetic energy are conserved. The objects bounce off each other with no permanent deformation, and no energy is lost as heat, sound, etc.
    • Inelastic collision: Momentum is conserved, but some kinetic energy is converted into heat, sound, or deformation. Total kinetic energy after the collision is less than before.

    (In every collision where no external force acts, momentum is conserved. Kinetic energy is conserved only in the elastic case.)

    Checking each option:

    • A. One of the objects was initially at rest: This doesn't decide whether KE is conserved. A moving ball can hit a stationary one and still lose energy as heat and sound. ✗
    • B. Potential energy is converted to work: This has nothing to do with conservation of kinetic energy in a collision. ✗
    • C. The collision is inelastic: In an inelastic collision, kinetic energy is not conserved. ✗
    • D. The collision is elastic: By definition, kinetic energy is conserved. ✓

    Answer: The correct option is D.

    Tip: Remember "Elastic = Energy conserved." Momentum is conserved in all collisions, but kinetic energy is conserved only in elastic ones.

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31. 31.

    The average distance moved by a molecule between collisions is called

    1. A.molecular distance
    2. B.intermolecular distance
    3. C.mean distance
    4. D.mean free path

    Show answer

    Answer: D. mean free path

    AI explanation

    Step 1: Analyze the question The question asks for the name of the average distance a molecule travels between one collision and the next. This comes from the kinetic theory of gases.

    Step 2: Explain the concept In a gas, molecules move randomly at high speeds and keep colliding with each other and with the walls of their container. Between collisions, a molecule travels in a straight line. The average length of these straight-line paths is called the mean free path.

    • "Mean" means average.
    • "Free" means the molecule moves freely, with no collision.
    • "Path" means the distance travelled.

    The mean free path depends on:

    • Pressure/density: at higher pressure or density, molecules are closer together, so the mean free path is shorter.
    • Molecular size: larger molecules collide more often, so the mean free path is shorter.
    • Temperature: at constant pressure, a higher temperature makes the gas less dense, so the mean free path is longer.

    Step 3: Check each option

    • A. Molecular distance: not a standard physics term.
    • B. Intermolecular distance: this is the separation between neighbouring molecules, not the distance travelled between collisions.
    • C. Mean distance: a vague term that is not used in kinetic theory.
    • D. Mean free path: this is the correct term, as defined above.

    Step 4: Answer The correct option is D. mean free path.

    Exam tip: Break the phrase into its words. "Average" gives mean, "between collisions" gives free, and "distance moved" gives path. Together they make mean free path.

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32. 32.

    What factors determine the frequency of a note emitted by a vibrating string?

    1. A.Amplitude of vibration, force constant of string and length of string
    2. B.Amplitude of vibration, force constant of string, and tension in string
    3. C.Mass per unit length of string, tension in string and length of string
    4. D.Force constant of string, tension in string, and length of string.

    Show answer

    Answer: C. Mass per unit length of string, tension in string and length of string

    AI explanation

    Analyze the question: We need the factors that determine the frequency of a note from a vibrating string (like a guitar or sonometer wire).

    Concept: For a stretched string fixed at both ends, the fundamental frequency is

    f = (1/2L) × √(T/μ)

    where:

    • L = length of the string
    • T = tension in the string
    • μ = mass per unit length of the string

    Step by step:

    1. The formula contains only L, T and μ, so these three factors determine the frequency.
    2. Amplitude does not appear in the formula. Plucking a string harder makes the note louder, not higher in pitch. This eliminates options A and B.
    3. "Force constant" (as in Hooke's law) is not a variable in the string frequency formula. This eliminates option D.
    4. Option C lists mass per unit length, tension and length, which matches the formula exactly.

    Answer: Option C is correct.

    Tip: Remember the three variables as L-T-μ: length, tension and mass per unit length.

    • Shorter string → higher frequency
    • Greater tension → higher frequency
    • Heavier (thicker) string → lower frequency

    This is why thick guitar strings give bass notes and tightening a string raises its pitch. Amplitude only affects loudness, never pitch.

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33. 33.

    The depolarising agent in a Leclanche cell is?

    1. A.carbon  rod
    2. B.ammonium chloride
    3. C.manganese (IV) oxide
    4. D.zinc plate

    Show answer

    Answer: C. manganese (IV) oxide

    AI explanation

    Analyze the question: It asks which substance in a Leclanché cell acts as the depolarising agent.

    Explain the concept: In a simple primary cell, hydrogen gas forms at the positive electrode (the carbon rod) as the cell works. This build-up of hydrogen bubbles is called polarisation. It insulates the electrode and increases the cell's internal resistance, so the current drops quickly.

    A depolarising agent is an oxidising substance that removes this hydrogen by oxidising it to water before it can build up.

    Parts of the Leclanché cell:

    • Zinc case/plate: negative electrode
    • Carbon rod: positive electrode (collects current)
    • Ammonium chloride paste: electrolyte
    • Manganese(IV) oxide (MnO₂): depolarising agent, packed around the carbon rod

    Step-by-step solution:

    1. Hydrogen forms at the carbon rod: 2H⁺ + 2e⁻ → H₂
    2. Manganese(IV) oxide oxidises this hydrogen: 2MnO₂ + H₂ → Mn₂O₃ + H₂O
    3. Since the hydrogen is removed, polarisation is prevented.

    So the depolarising agent is manganese(IV) oxide.

    • A. Carbon rod: it is the positive electrode, not the depolariser.
    • B. Ammonium chloride: it is the electrolyte.
    • D. Zinc plate: it is the negative electrode.

    Exam tip: Remember "Manganese Makes hydrogen Melt away", so MnO₂ is the depolariser. Also, a Leclanché cell is a primary cell with zinc as negative, carbon as positive, NH₄Cl as electrolyte, and MnO₂ as depolariser.

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34. 34.

    Which of the following actions would increase the electric force between two positively charged particles?

    1. A.Decreasing the mass of the particles
    2. B.Decreasing the distance between the particles
    3. C.Increasing the assistance between the particles
    4. D.Increasing the mass of the particles

    Show answer

    Answer: B. Decreasing the distance between the particles

    AI explanation

    Step 1: Analyze the question We need to find which action increases the electric force between two like (positive) charges.

    Step 2: The concept – Coulomb's Law

    F = kq₁q₂ / r²

    • F = electric force
    • q₁, q₂ = magnitudes of the charges
    • r = distance between the charges
    • k = Coulomb's constant (a fixed value)

    From the formula, the force depends on the charges and the distance. It does not depend on the mass of the particles. Also, force is inversely proportional to the square of the distance, so a smaller distance gives a larger force.

    Step 3: Check each option

    • A. Decreasing the mass: Mass does not appear in Coulomb's law, so there is no effect on the electric force. ❌
    • B. Decreasing the distance: Since F ∝ 1/r², reducing r makes F larger. For example, halving the distance makes the force 4 times bigger. ✅
    • C. Increasing the "assistance" (distance) between the particles: This is clearly a typo for "distance". Increasing r reduces the force. ❌
    • D. Increasing the mass: Again, mass has no role in Coulomb's law. ❌

    Step 4: Answer The correct option is B. Decreasing the distance between the particles.

    Tip: Remember "Close = Strong." For electric (and gravitational) forces, bringing objects closer increases the force by the inverse square of the distance. Mass only matters for gravitational force, not electric force. In WASSCE, whenever you see mass offered as an option in a Coulomb's law question, it is almost always a distractor.

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35. 35.

    A parallel plate capacitor is charged and the charging battery is subsequently disconnected. lf the plates of the capacitor are moved farther apart by means of insulating handles, the

    1. A.capacitance would increase
    2. B.capacitance would decrease
    3. C.charge on the capacitor would increase
    4. D.charge on the capacitor would decrease

    Show answer

    Answer: B. capacitance would decrease

    AI explanation

    Analyze the question: A charged capacitor is disconnected from the battery, so the charge has nowhere to go. Then the plates are pulled farther apart. We must decide what happens to the capacitance and the charge.

    Concept: For a parallel plate capacitor:

    C = ε₀A / d

    • C = capacitance
    • A = plate area
    • d = separation between the plates
    • ε₀ = permittivity of free space

    Capacitance is inversely proportional to the plate separation.

    Solution:

    1. The battery is disconnected, so the charge Q stays constant. There is no path for charge to flow on or off the plates. This rules out options C and D.
    2. The plates are moved farther apart, so d increases.
    3. Since C = ε₀A/d and A and ε₀ do not change, increasing d makes C decrease.

    Extra insight: with Q constant and C decreasing, the potential difference V = Q/C increases. The energy stored, ½QV, also increases. This is because you do work pulling the plates apart against their attraction.

    Checking the options:

    • A. Capacitance would increase: wrong, since d increases.
    • B. Capacitance would decrease: correct.
    • C. Charge would increase: wrong, since the battery is disconnected.
    • D. Charge would decrease: wrong, since the charge is trapped on the isolated plates.

    **Answer: B.

    Exam tip: Ask yourself whether the battery is connected or disconnected.

    • Disconnected: Q stays constant.
    • Connected: V stays constant.

    Also remember that C ∝ 1/d, so moving plates apart always lowers capacitance.

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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 temperature of an object is raised by 120°C. The resulting increase in its absolute temperature is

    1. A.50K
    2. B.120 K
    3. C.200K
    4. D.393K

    Show answer

    Answer: B. 120 K

    AI explanation

    Analyze the question The temperature rises by 120°C. We are asked for the corresponding increase on the absolute (Kelvin) scale. This is about a temperature change, not a temperature reading.

    Concept The Celsius and Kelvin scales are related by:

    T(K) = θ(°C) + 273

    The two scales have the same size of degree, so one degree Celsius step equals one kelvin step. The only difference between them is where zero is placed.

    Solution Suppose the initial temperature is θ₁ and the final temperature is θ₂, with θ₂ − θ₁ = 120°C.

    In Kelvin:

    • T₁ = θ₁ + 273
    • T₂ = θ₂ + 273

    Increase in absolute temperature: ΔT = T₂ − T₁ = (θ₂ + 273) − (θ₁ + 273) = θ₂ − θ₁ = 120 K

    The 273 cancels out, so a change of 120°C is exactly a change of 120 K.

    Answer The increase in absolute temperature is 120 K, which is option B.

    Why the other options are wrong

    • D (393 K) comes from adding 273 to 120. That would be the absolute temperature of an object at 120°C, not the increase in temperature.
    • A and C do not match any correct calculation.

    Exam tip When a question says "raised by," "increase in," or "change in" temperature, the number stays the same in °C and K. Only add 273 when the question gives an actual temperature reading, such as "at 120°C."

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38. 38.

    In an electric circuit, an inductor of inductance 0.5 H and resistance 50$\Omega$ is connected to an alternating current source of frequency 60 Hz. Calculate the impedance of the circuit.

    1. A.50.0$\Omega$
    2. B.450.5 $\Omega$
    3. C.195.0 $\Omega$
    4. D.1950.1 $\Omega$

    Show answer

    Answer: C. 195.0 $\Omega$

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39. 39.

    A luminous object is one that

    1. A.gives off dim blue-green light only in the dark.
    2. B.gives out light of its own
    3. C.shines by reflected light only
    4. D.glows only in the presence of light

    Show answer

    Answer: B. gives out light of its own

    AI explanation

    Step 1: Analyze the question The question asks for the definition of a luminous object in the study of light.

    Step 2: Explain the concept In Physics, objects are classified by how they relate to light:

    • Luminous objects produce their own light. Examples are the Sun, stars, a lit candle, and a glowing electric bulb.
    • Non-luminous objects do not produce light. We see them only because they reflect light from luminous sources. Examples are the Moon, a book, a table, and a mirror.

    Step 3: Evaluate each option

    • A. "Gives off dim blue-green light only in the dark" describes bioluminescence or phosphorescence, which is not the general definition of luminous. ❌
    • B. "Gives out light of its own" is exactly the definition of a luminous object. ✅
    • C. "Shines by reflected light only" describes a non-luminous object, like the Moon. ❌
    • D. "Glows only in the presence of light" does not describe a source of its own light. ❌

    Step 4: Answer The correct option is B.

    Tip: Remember that luminous contains the idea of luminance, or light. A luminous object is a light maker. A non-luminous object is only a light reflector. Whenever you see the Moon in a WASSCE question, think "non-luminous, because it reflects sunlight."

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40. 40.

    Which of the following statements about photoelectrons is correct?

    1. A.A faint green light produces photoelectrons with less kinetic energy than a bright red light
    2. B.A red light releases a smaller number of electrons than a green light
    3. C.A faint green light produces photoelectrons with greater kinetic energy than a bright red light
    4. D.A red light produces more photoelectrons than a green light

    Show answer

    Answer: C. A faint green light produces photoelectrons with greater kinetic energy than a bright red light

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41. 41.

    Which of the following statements about the motion of a simple pendulum is true?

    1. A.It is a simple harmonic motion when the angle of displacement is large
    2. B.It passes the equilibrium position with minimum speed
    3. C.It possesses maximum kinetic energy at the extreme positions
    4. D.lt swings faster at the poles than at the equator

    Show answer

    Answer: D. lt swings faster at the poles than at the equator

    AI explanation

    Analyze the question: We need to find the one true statement about a simple pendulum.

    Key concepts:

    • Period of a simple pendulum: T = 2π√(L/g)
    • SHM only occurs for small angles (below about 10°), because only then sin θ ≈ θ.
    • At the equilibrium (lowest) point, the speed is maximum and the kinetic energy is maximum.
    • At the extreme positions, the speed is zero, the kinetic energy is zero, and the potential energy is maximum.

    Check each option:

    • A. SHM when the angle is large: False. SHM requires small angles. For large angles the restoring force is not proportional to displacement.
    • B. Passes equilibrium with minimum speed: False. Speed is maximum at the equilibrium position.
    • C. Maximum kinetic energy at extreme positions: False. At the extremes the bob momentarily stops, so KE = 0 and PE is maximum.
    • D. Swings faster at the poles than at the equator: Consider g. It is larger at the poles (about 9.83 m/s²) than at the equator (about 9.78 m/s²), because the Earth is slightly flattened and also because of the Earth's rotation. Since T = 2π√(L/g), a larger g gives a smaller period, so the pendulum completes each swing in less time. It therefore swings faster (higher frequency) at the poles. True.

    Answer: D

    Tip: Remember "big g, short T." Anything that increases g (like going to the poles or to sea level) makes a pendulum oscillate faster. Also remember that for a pendulum, KE is maximum at the bottom, and PE is maximum at the ends.

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42. 42.

    Which of the following units is not fundamental?

    1. A.Metre
    2. B.Kilogram
    3. C.Joule
    4. D.Candela

    Show answer

    Answer: C. Joule

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43. 43.

    In photoelectric effect, the number of electrode emitted per second from a metallic surface is proportional to the

    1. A.intensity of the incident radiation
    2. B.frequency of the incident radiation
    3. C.energy of the incident radiation
    4. D.work function of the metal.

    Show answer

    Answer: A. intensity of the incident radiation

    AI explanation

    Step 1: Analyze the question The question asks what determines the number of electrons emitted per second (the photocurrent), not the energy of each electron.

    Step 2: The concept In the photoelectric effect, light behaves as a stream of photons, each carrying energy E = hf.

    • Frequency (f) decides whether emission happens at all (f must be at least the threshold frequency f₀) and sets the maximum kinetic energy of each electron: KE_max = hf − φ
    • Intensity is the number of photons arriving per second per unit area. Each photon can free at most one electron, so more photons per second means more electrons emitted per second.

    Step 3: Check each option

    • A. Intensity of the incident radiation: The number of photons per second is proportional to intensity, so the number of electrons emitted per second is proportional to intensity (provided f ≥ f₀). ✔
    • B. Frequency: This affects the kinetic energy of the electrons, not how many are emitted. ✘
    • C. Energy of the incident radiation: The energy of each photon depends on frequency, so this also affects electron energy rather than the number. ✘
    • D. Work function: This is a property of the metal that sets the threshold. It is not something the emission rate is proportional to. ✘

    Step 4: Answer The number of electrons emitted per second is proportional to the intensity of the incident radiation.

    Exam tip: Remember it this way:

    • Intensity → Number of electrons (photocurrent)
    • Frequency → Kinetic energy of electrons (and whether emission happens)

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44. 44.

    Water waves have a wavelength of 3.6cm and speed of 18cms$^{-1 }$ in deep water. If the waves enter shallow water with wavelength of 2.0cm, calculate the speed of the waves in the shallow water.

    1. A.0.4cms$^{-1}$
    2. B.2.5cms$^{-1}$
    3. C.10.0cms$^{-1}$
    4. D.10.8cms$^{-1}$

    Show answer

    Answer: C. 10.0cms$^{-1}$

    AI explanation

    Analyze the question: A wave moves from deep water into shallow water. We are given the wavelength and speed in deep water, and the wavelength in shallow water. We need the speed in shallow water.

    Concept: When a wave changes medium (or depth), its frequency stays the same, because the frequency is set by the source. Speed and wavelength change together, linked by:

    v = fλ, so v₁/λ₁ = v₂/λ₂

    Solution:

    Deep water:

    • λ₁ = 3.6 cm
    • v₁ = 18 cm/s

    Frequency: f = v₁/λ₁ = 18 / 3.6 = 5 Hz

    Shallow water:

    • λ₂ = 2.0 cm
    • f = 5 Hz (unchanged)

    v₂ = fλ₂ = 5 × 2.0 = 10.0 cm/s

    Check using the ratio: v₂ = v₁ × (λ₂/λ₁) = 18 × (2.0/3.6) = 10 cm/s ✓

    Answer: C. 10.0 cm/s

    Tip: When a wave crosses a boundary, remember that f stays constant, while v and λ change in the same proportion. Waves slow down in shallow water, so the wavelength gets shorter. Your answer should be less than 18 cm/s, which rules out any option above 18. Option D (10.8) comes from wrongly multiplying 18 by 0.6, so watch your ratios carefully.

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45. 45.

    The diagram above illustrates a ball of mass m sliding down a plank inclined at an angle of 0 to the horizontal. The kinetic friction between the ball and the plank is F and the acceleration of free fall is g. The net force on the ball along the plank is?

    

    1. A.mgsin $\theta$ + F
    2. B.F - mgcos $\theta$
    3. C.mgsin $\theta$ - F
    4. D.F + mgcos $\theta$

    Show answer

    Answer: C. mgsin $\theta$ - F

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46. 46.

    A 500N box rests on a horizontal floor. A constant horizontal force is exerted on the box so that it moves through 8m. If the coefficient of kinetic  friction between the floor and the box is 0.22, calculate the workdone on the box

    1. A.880J
    2. B.440J
    3. C.400J
    4. D.110J

    Show answer

    Answer: A. 880J

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47. 47.

    The vacuum between the double walls of a thermos flask reduces heat loss through

    1. A.conduction and radiation
    2. B.convection and conduction
    3. C.radiation only
    4. D.conduction only

    Show answer

    Answer: B. convection and conduction

    AI explanation

    Analyze the question: The thermos flask (vacuum flask) has a double wall with a vacuum in between. We need to know which heat transfer methods the vacuum stops.

    Explain the concept: There are three modes of heat transfer:

    • Conduction: heat passes through matter (solids, liquids, gases) by particle-to-particle collisions. It needs a material medium.
    • Convection: heat is carried by the movement of fluids (liquids or gases). It needs a material medium.
    • Radiation: heat travels as electromagnetic waves. It needs no medium and can cross a vacuum.

    Solution:

    1. A vacuum is a space with essentially no particles.
    2. With no particles, there is nothing to conduct heat by collisions, so conduction is prevented.
    3. With no air or fluid, there are no currents to carry heat, so convection is prevented.
    4. Radiation can still travel through a vacuum. That is why the flask's walls are silvered (shiny) to reflect radiant heat back. The vacuum itself does not stop radiation.

    So the vacuum reduces heat loss by conduction and convection.

    Answer: Option B, convection and conduction.

    Why the others are wrong:

    • A: Radiation is not stopped by a vacuum, so it is reduced only by the silvering.
    • C: Radiation is the one mode the vacuum cannot prevent.
    • D: Convection is also stopped, so "conduction only" is incomplete.

    Exam tip: Remember "Vacuum kills the medium." Conduction and convection need a medium, so the vacuum stops both. Radiation does not, which is why the Sun's heat reaches Earth through space. For a thermos flask, remember: vacuum → conduction and convection; silvered walls → radiation; stopper/cork → conduction and convection through the top.

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48. 48.

    The earpiece of a telephone handset converts energy from

    1. A.electrical to sound
    2. B.sound to electrical
    3. C.sound to electrical
    4. D.sound to radio wave

    Show answer

    Answer: A. electrical to sound

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49. 49.

    An electron of mass 9.1x 10$^{-31}$ kg is travelling at a speed of 2.0 x 10$^6$ms$^{-1}$. Calculate the associate wavelength of the electron. [h = 6.6. x 10$^{-34}$ Js]

    1. A.3.63 x10$^{-10}$ m
    2. B.3.63 x 10$^{-8}$ m
    3. C.3.63 x 10$^{-7}$ m
    4. D.6.89 x 10$^{-4}$ m

    Show answer

    Answer: A. 3.63 x10$^{-10}$ m

    AI explanation

    Analyze the question: We need the de Broglie wavelength of an electron moving at a known speed.

    Concept: Every moving particle has an associated wave with wavelength

    λ = h / (mv)

    where h is Planck's constant, m is the mass and v is the speed.

    Solution:

    1. Momentum: mv = (9.1 × 10⁻³¹ kg)(2.0 × 10⁶ m/s) = 18.2 × 10⁻²⁵ = 1.82 × 10⁻²⁴ kg m/s

    2. Wavelength: λ = (6.6 × 10⁻³⁴) / (1.82 × 10⁻²⁴)

    3. Divide the numbers: 6.6 / 1.82 ≈ 3.63

    4. Divide the powers of ten: 10⁻³⁴ / 10⁻²⁴ = 10⁻¹⁰

    λ ≈ 3.63 × 10⁻¹⁰ m

    Tip: In de Broglie questions, combine the mass and speed first to get the momentum, then divide h by it. For ordinary electrons, the wavelength is usually around 10⁻¹⁰ m (atomic size), so options with 10⁻⁷ or 10⁻⁴ are quickly ruled out.

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50. 50.

    A ray of light traveling from glass into ethyl alcohol is incident at the boundary at an angle of incidence 30$^o$. Calculate the angle of refraction. [Refractive index of glass =1.5; refractive index of ethyl alcohol = 1.36]

    1. A.27$^o$
    2. B.33.5$^o$
    3. C.51.7$^o$
    4. D.72.8$^o$

    Show answer

    Answer: B. 33.5$^o$

    AI explanation

    Analyze the question: Light moves from glass (n = 1.5) into ethyl alcohol (n = 1.36). Since alcohol is optically less dense, the ray bends away from the normal, so the angle of refraction must be greater than 30°.

    Concept: Snell's law: n₁ sin i = n₂ sin r

    Solution:

    1.5 × sin 30° = 1.36 × sin r

    1.5 × 0.5 = 1.36 × sin r

    0.75 = 1.36 × sin r

    sin r = 0.75 / 1.36 = 0.5515

    r = sin⁻¹(0.5515) ≈ 33.5°

    Check: sin 33.5° = 0.5519, which matches.

    Check against the options:

    • A (27°) is less than 30°, which is wrong because the ray should bend away from the normal.
    • C (51.7°) and D (72.8°) are too large.
    • B (33.5°) matches the calculation.

    Tip: Before calculating, check the direction of bending. Going from a higher index to a lower index means r > i (away from the normal), and going from a lower index to a higher index means r < i (towards the normal). This can eliminate options quickly. Also remember that sin 30° = 0.5 makes the calculation easy.

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