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WAEC (WASSCE) 2022

2022 WAEC (WASSCE) Physics Past Questions and Answers

The 2022 WAEC (WASSCE) Physics past questions with answers: 50 objective questions from the 2022 paper in the DeeepSolve question bank, each with its answer behind "Show answer". Try each question before you check, then practise the paper as a timed WAEC-style CBT.

Past questions © the examination body (JAMB/WAEC/NECO). DeeepSolve is not affiliated with them. Rights holders: see /copyright.

Questions

  1. 1.

    Which of the following concepts is a method of heat transfer that does not require a material medium?

    1. A.Conduction
    2. B.Diffusion
    3. C.Convection
    4. D.Radiation
    Show answer

    Answer: D. Radiation

    AI explanation

    Step 1: Analyze the question You are asked which method of heat transfer does not need a material medium (solid, liquid, or gas) to carry the heat.

    Step 2: Explain the concepts

    • Conduction: Heat passes from particle to particle by direct contact, mainly in solids. Particles must be present. Example: a metal spoon getting hot in a pot of soup.
    • Convection: Heat is carried by the movement of fluid (liquid or gas) particles. Example: boiling water, or sea breezes. It needs a fluid.
    • Diffusion: This is the spreading of particles from a region of high concentration to low concentration (like perfume spreading in a room). It is not a method of heat transfer, and it also needs a medium.
    • Radiation: Heat is transferred by electromagnetic waves (mainly infrared). These waves can travel through a vacuum, so no medium is needed. Example: the Sun's heat reaching Earth across empty space.

    Step 3: Solution

    • Conduction needs a medium, so it is ruled out.
    • Diffusion needs a medium and is not a heat transfer method, so it is ruled out.
    • Convection needs a fluid, so it is ruled out.
    • Radiation travels as electromagnetic waves and needs no medium, so it fits.

    Answer: D. Radiation

    Tip: Remember "Sun to Earth = Radiation." Space is a vacuum, so the only way the Sun's heat reaches us is a method that needs no medium. Also, conduction and convection both need particles: conduction for solids, convection for fluids.

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  2. 2.

    The engine of a car provides a forward force of 1240 N and the total resistive force on the car is 800N. If the mass of the car is 1220 kg, determine the distance the car has to travel from the rest before acquiring a speed of 4 m s−1^{-1}.

    1. A.44.0 m
    2. B.22.2 m
    3. C.11.1 m
    4. D.5.5 m
    Show answer

    Answer: B. 22.2 m

    AI explanation

    Analyze the question: A car starts from rest. A forward force of 1240 N acts on it while a resistive force of 800 N opposes the motion. We need the distance travelled before its speed reaches 4 m/s.

    Concept: Newton's second law gives the acceleration from the net force, F_net = ma. Then we use the equation of motion v² = u² + 2as.

    Solution:

    1. Net force = 1240 − 800 = 440 N
    1. Acceleration: a = F_net / m = 440 / 1220 ≈ 0.3607 m/s²
    1. Use v² = u² + 2as with u = 0 and v = 4: 16 = 2(0.3607)s s = 16 / 0.7213 ≈ 22.18 m

    Alternatively, using the work-energy theorem: Net force × distance = ½mv² 440 × s = ½ × 1220 × 16 = 9760 s = 9760 / 440 ≈ 22.2 m

    Answer: The distance is about 22.2 m, which is option B.

    Tip: In "net force" problems, always subtract the resistive force first. Then you can use either F = ma with the equations of motion, or the work-energy method (Fs = ½mv²). The work-energy method skips finding acceleration, so it saves time in the exam.

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  3. 3.

    The periodic rise and fall in the intensity of sound produced whn two notes of nearly equal frequencies are sounded together is called?

    1. A.doppler effect
    2. B.beat
    3. C.interference
    4. D.resonance
    Show answer

    Answer: B. beat

    AI explanation

    Step 1: Analyze the question The question describes two sound notes with nearly equal frequencies played together. The result is a periodic rise and fall in loudness (intensity). We need the name of this phenomenon.

    Step 2: Explain the concept When two waves of slightly different frequencies, f₁ and f₂, travel together, they alternately reinforce each other (constructive interference) and cancel each other (destructive interference). This produces a regular "waa-waa-waa" pulsing in loudness. Each pulse is called a beat.

    The beat frequency is:

    f_beat = |f₁ − f₂|

    For example, if two tuning forks of 256 Hz and 260 Hz sound together, you hear 4 beats per second.

    Step 3: Check each option

    • A. Doppler effect: An apparent change in frequency due to relative motion between source and observer (e.g., an ambulance siren changing pitch as it passes). This is not the case here.
    • B. Beat: The periodic rise and fall in loudness from two nearly equal frequencies. This matches the description.
    • C. Interference: This is the general superposition of waves. It is the underlying cause of beats, but it does not specifically describe the periodic variation in intensity from two close frequencies.
    • D. Resonance: This occurs when an object vibrates at its natural frequency because of an external driving vibration of the same frequency. This is not the case here.

    Step 4: Answer The correct option is B. beat.

    Exam tip: Whenever you see "two nearly equal frequencies" together with "rise and fall in loudness," think beats. Remember the formula: beat frequency = difference between the two frequencies.

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  4. 4.

    Which of the illustrated graphs above represents a body moving with uniform retardation?

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

    Answer: C. C

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  5. 5.

    A galvanometer with a full-scale deflection of 20 mA is Converted to read 8 K by connecting a 395 Ω\Omega resistor in series with it. Determine the internal resistance of the galvanometer

    1. A.2.5Ω\Omega
    2. B.5.0Ω\Omega
    3. C.8.0Ω\Omega
    4. D.10.0Ω\Omega
    Show answer

    Answer: B. 5.0Ω\Omega

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  6. 6.

    A quantity of water at 0 °C is heated to 30 °C. For each degree rise in temperature, its density will---------

    1. A.rise steadily
    2. B.fall steadily
    3. C.fall and then rises
    4. D.rise and then falls
    Show answer

    Answer: D. rise and then falls

    AI explanation

    Analyze the question: Water is heated from 0 °C to 30 °C. We need to know how its density changes over this range.

    Concept: the anomalous expansion of water

    Most liquids expand when heated, so their density falls steadily. Water behaves differently between 0 °C and 4 °C:

    • From 0 °C to 4 °C, water contracts as it is heated, so its volume decreases and its density increases.
    • At 4 °C, water has its minimum volume and therefore its maximum density (1000 kg/m³).
    • Above 4 °C, water expands normally, so its volume increases and its density decreases.

    Solution (step by step):

    1. At 0 °C, the density of water is about 999.8 kg/m³.
    2. Heating to 4 °C: the density rises to its maximum of about 1000 kg/m³.
    3. Heating from 4 °C to 30 °C: the density falls steadily (about 995.7 kg/m³ at 30 °C).

    So the density first rises and then falls.

    Checking the options:

    • A. Rise steadily: wrong, because it falls after 4 °C.
    • B. Fall steadily: wrong, because it rises between 0 °C and 4 °C.
    • C. Fall and then rises: this is the reverse of what happens. It describes the volume of water, not the density.
    • D. Rise and then falls: correct.

    Exam tip: Remember that 4 °C is the turning point. At 4 °C, water has its minimum volume and maximum density. Volume and density behave in opposite ways, so if a question asks about volume, flip the answer: volume falls and then rises, while density rises and then falls. This is also why ice floats and why fish survive in the water under frozen lakes.

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  7. 7.

    Which of the following descriptions of the image formed by a plane mirror is not correct. the image is----

    1. A.erect and of the same size as the object
    2. B.laterally inverted and of the same size as the object
    3. C.erect and bigger than the object
    4. D.virtual and if the same size
    Show answer

    Answer: C. erect and bigger than the object

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  8. 8.

    One major reason why electrical appliances in homes are normally earthed is that the-----------

    1. A.person touching the appliance is safe from electric shock
    2. B.appliances are maintained at a higher p.d. than the earth
    3. C.appliances are maintained at a lower p.d. than the earth
    4. D.appliances are maintained at the same p.d. with that of the earth
    Show answer

    Answer: A. person touching the appliance is safe from electric shock

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  9. 9.

    Molecules move in random motion within a liquid. The total internal energy of the liquid depends on all of the following except its?

    1. A.temperature
    2. B.mass
    3. C.specific heat capacity
    4. D.melting point
    Show answer

    Answer: D. melting point

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  10. 10.

    A freely suspended compass needle on the earth's surface settles in a plane called----------

    1. A.geographic meridian
    2. B.magnetic meridian
    3. C.magnetic declination
    4. D.isoganals
    Show answer

    Answer: B. magnetic meridian

    AI explanation

    Analyze the question: It asks for the name of the vertical plane in which a freely suspended magnet (compass needle) comes to rest under the earth's magnetic field.

    Concept:

    • Geographic meridian: the vertical plane passing through the geographic north and south poles and the point of observation.
    • Magnetic meridian: the vertical plane containing the earth's magnetic field at a place, which is the plane in which a freely suspended magnet rests.
    • Magnetic declination (variation): the angle between the geographic meridian and the magnetic meridian. It is an angle, not a plane.
    • Isogonals: lines on a map joining places that have the same magnetic declination. (The option is spelled "isoganals", but this is what it means.)

    Solution:

    1. A freely suspended needle aligns itself along the earth's magnetic field direction.
    2. The vertical plane containing this needle is, by definition, the magnetic meridian.
    3. Option A is wrong because the geographic meridian is defined by the geographic poles. The needle only lines up with it where the declination is zero.
    4. Option C is wrong because declination is an angle, not a plane.
    5. Option D is wrong because isogonals are lines on a map, not a plane.

    **Correct answer: B, magnetic meridian.

    Tip: Remember "Magnet rests in Magnetic meridian." Also remember that declination is the angle between the two meridians, and dip (inclination) is the angle the field makes with the horizontal.

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  11. 11.

    When the direction of vibration of the particles of a medium is perpendicular to the direction of propagation of a wave, the wave is said to be--------

    1. A.longitudinal
    2. B.transverse
    3. C.mechanical
    4. D.a sound wave
    Show answer

    Answer: B. transverse

    AI explanation

    Step 1: Analyze the question The question describes the relationship between two directions:

    • The direction in which the particles of the medium vibrate
    • The direction in which the wave travels (propagates)

    Here, the two are perpendicular (at 90° to each other).

    Step 2: Explain the concept Waves are classified by how particles vibrate relative to the wave's direction of travel:

    | Type | Particle vibration vs. wave direction | Examples | |---|---|---| | Transverse | Perpendicular (90°) | Water waves, light and other electromagnetic waves, waves on a string | | Longitudinal | Parallel (along the same line) | Sound waves, compressions and rarefactions in a spring |

    Step 3: Check each option

    • A. Longitudinal: Wrong. Here the vibration is parallel to the direction of propagation.
    • B. Transverse: Correct. Perpendicular vibration is the definition of a transverse wave.
    • C. Mechanical: Wrong. This describes waves that need a medium, and it does not say anything about the vibration direction. Both transverse and longitudinal waves can be mechanical.
    • D. A sound wave: Wrong. Sound in air is longitudinal.

    Step 4: Answer The wave is transverse, which is option B.

    Exam tip: Remember "T = Trans = Across." Transverse waves vibrate across the direction of travel, like a crest and trough on a rope. For longitudinal waves, think of "L = Along", as in compressions and rarefactions along the line of travel.

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  12. 12.

    Gamma rays are produced when?

    1. A.high velocity electrons are abruptly stopped in metals
    2. B.energy changes occur within the nuclei of atoms
    3. C.energy changes occur within the electronic structure of atoms
    4. D.electrons are deflected in very strong magnetic fields
    Show answer

    Answer: B. energy changes occur within the nuclei of atoms

    AI explanation

    Step 1: Analyze the question We need to identify the origin of gamma rays among the four options.

    Step 2: Explain the concept Different electromagnetic radiations come from different processes:

    • X-rays are produced when high-speed electrons are suddenly stopped by a metal target (bremsstrahlung), or when inner-shell electrons change energy levels.
    • Ultraviolet, visible and infrared light come from changes in the energy levels of the outer electrons of atoms.
    • Gamma rays come from the nucleus. After radioactive decay (alpha or beta), the daughter nucleus is often left in an excited state. When it drops to a lower energy state, it emits a high-energy photon, which is a gamma ray.

    Step 3: Check each option

    • A. This describes X-ray production, so it is wrong.
    • B. Energy changes within the nucleus produce gamma rays, so this is correct.
    • C. Energy changes in the electronic structure produce UV, visible light or X-rays, so it is wrong.
    • D. Deflection of electrons in magnetic fields produces synchrotron radiation, not gamma rays in this context, so it is wrong.

    Step 4: Answer

    Exam tip: Remember "Gamma = Nucleus". X-rays involve electrons (stopping or inner shells), while gamma rays involve the nucleus. Whenever you see "nuclear energy level change" or "de-excitation of the nucleus", think gamma.

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  13. 13.

    The speed of fast-moving neutrons in a nuclear reactor can be reduced by using?

    1. A.graphite rods
    2. B.concrete shield
    3. C.iron rods
    4. D.boron rods
    Show answer

    Answer: A. graphite rods

    AI explanation

    Analyze the question: The question asks which material slows down (reduces the speed of) fast neutrons in a reactor. The material that does this is called a moderator.

    Concept:

    • Moderator: slows fast neutrons to thermal speeds so they can cause further fission in uranium-235. Examples are graphite, heavy water (D₂O), and ordinary water.
    • Control rods: absorb neutrons to control the reaction rate. Examples are boron and cadmium.
    • Shield: thick concrete (often with lead) absorbs radiation to protect workers.

    Going through the options:

    • A. Graphite rods: graphite is a classic moderator. Neutrons collide with carbon atoms and lose kinetic energy without being absorbed much. ✔
    • B. Concrete shield: it protects against radiation and does not control the neutron speed in the core. ✘
    • C. Iron rods: iron is a structural material and not used as a moderator. ✘
    • D. Boron rods: boron absorbs neutrons and acts as a control rod, which regulates the number of neutrons rather than slowing them. ✘

    Answer: The correct option is A. graphite rods.

    Exam tip: Remember "Moderator = Slows, Control rod = Absorbs". Graphite and heavy water slow neutrons down, while boron and cadmium absorb neutrons and stop the reaction.

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  14. 14.

    The diameter of a brass ring at 30 °C is 50.0 cm. To what temperature must this ring be heated to increase its diameter to 50.29 cm? [ linear expansivity of brass = 1.9 x 10−5^{-5} K−1^{-1}]

    1. A.152.6 °C
    2. B.182.6 °C
    3. C.306.1 °C
    4. D.335.3 °C
    Show answer

    Answer: D. 335.3 °C

    AI explanation

    Analyze the question: A brass ring expands when heated. We know its original diameter, its new diameter, and its linear expansivity, and we need the final temperature.

    Concept: Linear expansion is given by

    ΔL = L₀ · α · Δθ

    so Δθ = ΔL / (L₀ · α)

    Solution:

    • L₀ = 50.0 cm
    • L = 50.29 cm
    • ΔL = 50.29 − 50.0 = 0.29 cm
    • α = 1.9 × 10⁻⁵ K⁻¹

    Δθ = 0.29 / (50.0 × 1.9 × 10⁻⁵)

    Denominator: 50.0 × 1.9 × 10⁻⁵ = 9.5 × 10⁻⁴

    Δθ = 0.29 / (9.5 × 10⁻⁴) = 305.26 K

    Final temperature = 30 + 305.26 = 335.26 °C ≈ 335.3 °C

    Answer: The ring must be heated to about 335.3 °C, which is option D.

    Option C (306.1 °C) is a common trap. It comes from finding only the temperature change (about 305 K) and forgetting to add the starting temperature of 30 °C.

    Tip: In thermal expansion questions, always ask yourself, "Is the question asking for the change in temperature or the final temperature?" If it asks "to what temperature," add the change to the initial temperature.

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  15. 15.

    The correct relationship between the displacement, s, of a particle initially at rest in a linear motion and the time, t, is?

    1. A.s α\alpha t−2^{-2}
    2. B.s α\alpha t−1^{-1}
    3. C.s α\alpha t
    4. D.s α\alpha t2^{2}
    Show answer

    Answer: D. s α\alpha t2^{2}

    AI explanation

    Analyze the question: A particle starts from rest (u = 0) and moves in a straight line. We need the relationship between displacement s and time t. The question doesn't say the acceleration is constant, but the standard assumption for this type of question is uniform acceleration.

    Concept: For uniform acceleration, the equation of motion is

    s = ut + ½at²

    Solution:

    1. The particle starts from rest, so u = 0.
    2. Substitute into the equation:

    s = (0)t + ½at² = ½at²

    1. Since ½ and a are constants (uniform acceleration), we can write:

    s ∝ t²

    So displacement is directly proportional to the square of time. This means if time doubles, displacement becomes four times as large.

    Checking the other options:

    • A (t⁻²) and B (t⁻¹): these would mean displacement decreases as time increases, which is wrong for a particle moving away from rest.
    • C (t): this applies to motion at constant velocity (s = vt), but our particle starts from rest and so must accelerate.
    • D (t²): matches s = ½at².

    Answer: D. s ∝ t²

    Tip: When you see "initially at rest," set u = 0 immediately. Then s = ½at² (s ∝ t²), v = at (v ∝ t), and v² = 2as (v² ∝ s). A graph of s against t² will be a straight line through the origin, and this is a common WASSCE graph question.

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  16. 16.

    Which of the following statement(s) is/are correct about a fixed mass of gas compressed in an inexpansible container; I. The average speed of the molecules increases II. The temperature of the gas increases III. The molecules hit the walls of the container more often than before the compression

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

    Answer: C. I, II, and III only

    AI explanation

    Analyzing the question

    A fixed mass of gas is compressed in a container. The question asks which of three statements are correct. This is about the kinetic theory of gases and the gas laws.

    Key concepts

    • When a gas is compressed (volume reduced), work is done on it. If this happens quickly (adiabatically, with no time for heat to escape), the internal energy of the gas increases.
    • For an ideal gas, temperature is proportional to the average kinetic energy of the molecules: KE = (3/2)kT. So higher temperature means higher average molecular speed.
    • Reduced volume means the molecules are closer together and travel shorter distances between collisions with the walls, so the collision rate with the walls increases. This is why pressure rises.

    Checking each statement

    • I. The average speed of the molecules increases. Compressing the gas does work on it and raises its internal energy. This increases the average kinetic energy, so the average speed goes up. ✔
    • II. The temperature of the gas increases. Temperature is a measure of average kinetic energy, so it rises too. ✔
    • III. The molecules hit the walls more often. The volume is smaller, so the molecules reach the walls more frequently. The faster speed adds to this effect. ✔

    All three statements are consistent with compressing the gas (the standard WASSCE assumption is that the compression is rapid, so the gas is not kept at constant temperature).

    Caution: If the compression were slow and isothermal (temperature held constant), I and II would not hold. The question's wording, with statements I and II included alongside III, implies the usual adiabatic treatment.

    Answer: C. I, II, and III only

    Exam tip: Remember the chain: compress → work done on gas → internal energy up → temperature up → faster molecules → more frequent wall collisions → pressure up. If a question says "slowly" or "constant temperature," only the collision frequency (III) increases. Look for those keywords.

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  17. 17.

    Three cells each of emf, 1.0 V, and internal resistance, 2 Ω\Omega, are connected in parallel across a 3Ω\Omega  resistor. Determine the current in the resistor.

    1. A.0.90A
    2. B.0.39A
    3. C.0.30A
    4. D.0.01A
    Show answer

    Answer: A. 0.90A

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  18. 18.

    An object is placed at different distances, u, from a converging lens of focal length, 15.0cm. For what value of u does the lens act as a microscope?

    1. A.u = 15cm only
    2. B.u = 30cm only
    3. C.M < 15cm only
    4. D.u > 30cm only
    Show answer

    Answer: C. M < 15cm only

    AI explanation

    Note: option C is printed as "M < 15cm only", which looks like a typo for "u < 15cm only". I'll treat it that way.

    Analyze the question

    A converging lens acts as a simple microscope (magnifying glass) when it produces an image that is enlarged, upright, and virtual. We need the range of object distances u that gives this.

    Concept

    For a converging lens with focal length f = 15.0 cm, the image depends on where the object is placed:

    • u > 2f (u > 30 cm): real, inverted, diminished image (like a camera)
    • u = 2f (u = 30 cm): real, inverted, same size image
    • f < u < 2f (15 to 30 cm): real, inverted, magnified image (like a projector)
    • u = f (u = 15 cm): image at infinity
    • u < f (u < 15 cm): virtual, upright, magnified image (magnifying glass)

    Solution

    Use the lens formula: 1/f = 1/u + 1/v

    So 1/v = 1/f − 1/u = (u − f)/(uf)

    • If u < f, then (u − f) is negative, so v is negative. This means the image is virtual, on the same side as the object.
    • The magnification is m = |v/u| = f/(f − u), which is greater than 1 whenever u < f. So the image is magnified and upright.

    For example, if u = 10 cm: 1/v = 1/15 − 1/10 = −1/30, so v = −30 cm. The magnification is 3, and the image is virtual, upright and enlarged.

    So the lens acts as a simple microscope only when u < 15 cm.

    Answer

    Option C (u < 15 cm only).

    Tip

    Remember "inside the focal length = magnifying glass." Whenever the object is closer to the lens than f, you get a virtual, upright, enlarged image. Cameras use u > 2f, and projectors use f < u < 2f.

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  19. 19.

    Arrange the following radiations in order of increasing ionization of air. I. Alpha Il. Gamma IIl. Beta

    1. A.I < III < II
    2. B.II < I < III
    3. C.II < III < I
    4. D.I < II
    Show answer

    Answer: C. II < III < I

    AI explanation

    Analyze the question: We need to rank alpha, beta and gamma radiation by how strongly they ionize air, from the weakest ionizer to the strongest.

    Concept: Ionizing power depends on how strongly the radiation interacts with air molecules, which depends on its charge, mass and speed.

    • Alpha (α): Helium nucleus with charge +2 and a large mass. It moves relatively slowly and interacts strongly with air molecules, so it has the highest ionizing power. It is stopped by a sheet of paper or a few cm of air.
    • Beta (β): Fast electron with charge -1 and a small mass. It has moderate ionizing power and is stopped by a few mm of aluminium.
    • Gamma (γ): Electromagnetic wave with no charge and no mass. It has the lowest ionizing power but the highest penetrating power. It is reduced by thick lead or concrete.

    Solution:

    Ionizing power: Alpha > Beta > Gamma

    Arranging in increasing order:

    Gamma (II) < Beta (III) < Alpha (I)

    That is: II < III < I

    Check against the options:

    • A. I < III < II: this is the decreasing order, so it is wrong.
    • B. II < I < III: this puts beta above alpha, so it is wrong.
    • C. II < III < I: this matches our result.
    • D. I < II: this is incomplete and wrong.

    Exam tip: Ionizing power and penetrating power are opposites. Remember "A-B-G" for ionizing power going down (Alpha, Beta, Gamma), and "G-B-A" for penetrating power going down. Always check whether the question asks for increasing or decreasing order, because that is where students lose marks.

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  20. 20.

    The viscosity of a fluid depends on the following factors except the?

    1. A.relative motion between the layers of the fluid
    2. B.nature of the material of the fluid
    3. C.surface area of the fluid in contact
    4. D.normal reaction in the fluid
    Show answer

    Answer: D. normal reaction in the fluid

    AI explanation

    Analyze the question: We need the factor that does NOT affect a fluid's viscosity.

    Concept: Viscosity is the internal friction of a fluid, which is its resistance to the relative motion of its layers. Newton's law of viscosity gives:

    F = ηA(dv/dx)

    where

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

    Going through the options:

    • A. Relative motion between the layers: The viscous force exists because adjacent layers move relative to each other, and it depends on the velocity gradient. This is a factor.
    • B. Nature of the material of the fluid: η is a property of the fluid itself (honey is far more viscous than water), and it also changes with temperature. This is a factor.
    • C. Surface area of the fluid in contact: In F = ηA(dv/dx), the viscous force is proportional to the contact area between the layers. Textbook treatments of this WASSCE question list it as a factor, so it counts as a dependence.
    • D. Normal reaction in the fluid: Viscosity arises from molecular interactions between layers moving relative to each other. It does not depend on a "normal reaction". That idea belongs to solid friction, where friction = μR. This is not a factor.

    Tip: Do not confuse viscosity with solid friction. Solid friction depends on the normal reaction (F = μR) and is independent of area. Viscous force depends on area, velocity gradient and the nature of the fluid, and has nothing to do with normal reaction.

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  21. 21.

    If the kinetic energy of an electron is 100 eV, what is the wavelength of the de-Broglie wave associated with it? [h = 6.6 x 10−34^{-34} J s, e = 1.6 x 10−19^{-19}C, me_{e}, = 9.1 x 10−31^{-31} kg]

    1. A.1.22 x 10−10^{-10}m
    2. B.4.10 x 10−10^{-10}m
    3. C.3.90 x 10−10^{-10}m
    4. D.5.50 x 10−14^{-14}m
    Show answer

    Answer: A. 1.22 x 10−10^{-10}m

    AI explanation

    Analyze the question: We need the de-Broglie wavelength of an electron whose kinetic energy is 100 eV.

    Concept: The de-Broglie wavelength is λ = h/p, where p is the momentum. Since KE = p²/2m, we get p = √(2mKE), so

    λ = h / √(2 m KE)

    Solution:

    1. Convert the energy to joules: KE = 100 × 1.6 × 10⁻¹⁹ = 1.6 × 10⁻¹⁷ J
    1. Find 2m·KE: 2 × 9.1 × 10⁻³¹ × 1.6 × 10⁻¹⁷ = 29.12 × 10⁻⁴⁸ = 2.912 × 10⁻⁴⁷
    1. Take the square root: √(2.912 × 10⁻⁴⁷) = √(29.12 × 10⁻⁴⁸) = 5.396 × 10⁻²⁴ kg m/s
    1. Find the wavelength: λ = 6.6 × 10⁻³⁴ / 5.396 × 10⁻²⁴ ≈ 1.22 × 10⁻¹⁰ m

    Answer: The wavelength is about 1.22 × 10⁻¹⁰ m, which is option A.

    Tip: For electrons, a handy shortcut is λ ≈ 1.226/√V nm, where V is the accelerating voltage (or the energy in eV). For 100 eV: 1.226/10 = 0.1226 nm = 1.22 × 10⁻¹⁰ m. Also, remember to convert eV to joules before using the formula, as forgetting this is the most common mistake.

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  22. 22.

    Which of the following statements-about electromagnetic waves is not correct?

    1. A.They carry energy as they travel through space
    2. B.They travel with the speed of light
    3. C.They are longitudinal
    4. D.The electric and magnetic fields are at right angles to each other
    Show answer

    Answer: C. They are longitudinal

    AI explanation

    Step 1: Analyze the question We need the statement that is NOT correct about electromagnetic (EM) waves.

    Step 2: Key concept EM waves (radio waves, light, X-rays, gamma rays, etc.) are made of oscillating electric and magnetic fields. These fields:

    • are perpendicular to each other,
    • are both perpendicular to the direction the wave travels.

    This makes EM waves transverse, not longitudinal.

    Step 3: Check each option

    • A. They carry energy as they travel through space. Correct. Sunlight carries energy to Earth.
    • B. They travel with the speed of light. Correct. In a vacuum, all EM waves travel at c = 3.0 × 10⁸ m/s.
    • C. They are longitudinal. Not correct. EM waves are transverse. Longitudinal waves, such as sound, need a medium and have vibrations along the direction of travel.
    • D. The electric and magnetic fields are at right angles to each other. Correct. This is the standard description of an EM wave.

    Step 4: Answer

    Tip: Remember "EM = Transverse". Light can be polarised, and only transverse waves can be polarised. Also remember that sound is longitudinal and needs a medium, whereas EM waves can travel through a vacuum.

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  23. 23.

    Which of the following statements about a straight current-carrying wire placed in a uniform magnetic field is correct? The wire experiences ---------------

    1. A.maximum motor force if the current reverses its direction
    2. B.no motor force of it is parallel to the field
    3. C.no motor force if it is perpendicular to the field
    4. D.a motor force with constant direction if either the current or the magnetic field is reversed
    Show answer

    Answer: B. no motor force of it is parallel to the field

    AI explanation

    Analyze the question: We need the true statement about the force (the "motor force") on a current-carrying wire in a uniform magnetic field.

    Concept: The force on a straight wire is

    F = B I L sin θ

    where θ is the angle between the wire (current direction) and the magnetic field. The direction of the force is given by Fleming's Left-Hand Rule, and it is perpendicular to both the current and the field.

    Checking each option:

    • A. Maximum force if the current reverses direction. Wrong. Reversing the current reverses the direction of the force. It does not make the force maximum.
    • B. No motor force if it is parallel to the field. Correct. When the wire is parallel to the field, θ = 0°, so sin 0° = 0 and F = 0. (The "of" in the option is a typo for "if".)
    • C. No motor force if it is perpendicular to the field. Wrong. When θ = 90°, sin 90° = 1, so the force is at its maximum, not zero.
    • D. Motor force with constant direction if either current or field is reversed. Wrong. Reversing either one reverses the force direction. (Reversing both together would leave the direction unchanged.)

    Answer: B.

    Tip: Remember "parallel = zero, perpendicular = maximum" for the force on a wire in a magnetic field. The wire must cut across the field lines to feel a force. If it runs along them, nothing happens.

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  24. 24.

    A hunter fires a gun at a point 408 m away from a cliff. If he hears an echo 2.4 s later, determine the speed of the sound wave

    1. A.340 ms−1^{-1}
    2. B.380 m s−1^{-1}
    3. C.400 m s −1^{-1}
    4. D.680 m s−1^{-1}
    Show answer

    Answer: A. 340 ms−1^{-1}

    AI explanation

    Analyze the question: Sound travels from the hunter to the cliff and back again, so the total distance covered is twice the distance to the cliff.

    Concept: For an echo,

    speed = total distance ÷ time = 2d / t

    Solution:

    • Distance to cliff, d = 408 m
    • Time for echo, t = 2.4 s
    • Total distance = 2 × 408 = 816 m

    v = 816 / 2.4 = 340 m/s

    Answer: The speed of the sound wave is 340 m/s.

    Why not D? Option D (680 m/s) is what you get if you forget that the sound travels there and back and use 408/2.4 × 4, or a similar slip. The most common mistake is using 408 m alone, which gives 170 m/s. That isn't an option, but it shows why you must double the distance.

    Tip: In every echo question, remember "there and back": use 2d = vt. Also, 340 m/s is the typical speed of sound in air, so if your answer lands near this value, it's a good sign you've done it right.

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  25. 25.

    Which of the following statements about electric potential energy is not correct?

    1. A.The electric potential energy of a positively charged particle increases when it moves to a point of higher potential
    2. B.The electric potential energy of a negatively charged particle increases when it moves to a point of lower potential
    3. C.The electric potential energy of a positively charged particle decreases when it moves to a point of higher potential
    4. D.The work done in taking a charged particle around a closed path in an electric field is zero.
    Show answer

    Answer: C. The electric potential energy of a positively charged particle decreases when it moves to a point of higher potential

    Get a step-by-step AI explanation in the app

  26. 26.

    An example of a mechanical wave is---------

    1. A.water waves
    2. B.radio waves
    3. C.x-rays
    4. D.light rays
    Show answer

    Answer: A. water waves

    AI explanation

    Step 1: Analyze the question The question asks which option is a mechanical wave.

    Step 2: Explain the concept

    • A mechanical wave needs a material medium (solid, liquid, or gas) to travel. It transfers energy by making the particles of the medium vibrate. Examples: sound waves, water waves, waves on a string, seismic waves.
    • An electromagnetic wave does not need a medium. It can travel through a vacuum, such as the space between the Sun and the Earth. Examples: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.

    Step 3: Check each option

    • A. Water waves: These travel through water, and the water particles vibrate as the wave passes. They need a medium, so they are mechanical.
    • B. Radio waves: These are part of the electromagnetic spectrum and need no medium, so they are not mechanical.
    • C. X-rays: These are high-frequency electromagnetic waves, so they are not mechanical.
    • D. Light rays: Light is electromagnetic and travels through a vacuum, so it is not mechanical.

    Step 4: Answer The correct option is A. water waves.

    Exam tip: Ask yourself, "Can it travel through empty space?" If yes, it is electromagnetic. If no, it is mechanical. Remember that all the waves in the electromagnetic spectrum (radio, microwave, infrared, light, UV, X-ray, gamma) are not mechanical. Sound is the other mechanical wave that often appears in WASSCE questions.

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  27. 27.

    The reason for having a large number of turns in the coil of a moving coil galvanometer is to--------

    1. A.make the deflection of the needle proportional to the current
    2. B.increase the sensitivity of the galvanometer
    3. C.decrease the magnetic flux produced by the magnet
    4. D.make the permanent magnet stronger
    Show answer

    Answer: B. increase the sensitivity of the galvanometer

    AI explanation

    Analyze the question: It asks why a moving coil galvanometer's coil has many turns.

    Concept: The torque on a coil carrying current I in a magnetic field is

    τ = N B I A

    where N is the number of turns, B the magnetic flux density, I the current, and A the area of the coil.

    This torque is balanced by the restoring torque of the hairsprings, kθ. So at equilibrium:

    NBIA = kθ, which gives θ = (NBA / k) I

    The current sensitivity is therefore:

    θ / I = NBA / k

    Working through the options:

    • A. The deflection is proportional to current because of the radial magnetic field (concave pole pieces and soft iron core) and the linear restoring spring. The number of turns does not cause this, so A is wrong.
    • B. Since θ/I = NBA/k, increasing N directly increases the deflection for a given current. This increases the sensitivity, so B is correct.
    • C. The coil does not reduce the magnet's flux, and more turns do not change the flux produced by the magnet, so C is wrong.
    • D. The coil has no effect on the strength of the permanent magnet, so D is wrong.

    Answer: B. Increase the sensitivity of the galvanometer

    Exam tip: Remember the sensitivity formula, NBA/k. To make a galvanometer more sensitive, you increase N, B and A, or use a weaker spring (smaller k). Also remember that the radial field is what makes the scale linear, which is the point of option A. WASSCE often tests this contrast.

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  28. 28.

    The distance between the fixed points of a mercury-in-glass thermometer is 30 cm. Determine the temperature when the mercury level is 10.5 cm above the lower fixed point

    1. A.28.6ºC
    2. B.30.0 ºC
    3. C.35.0 ºC
    4. D.40.5 ºC
    Show answer

    Answer: C. 35.0 ºC

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  29. 29.

    The efficiency of a wheel and axle is 100% and the ratio of their radii is 5:1. calculate the effort required to lift a load of mass 20kg using this machine, [g = 10 m s−2^{-2}]

    1. A.20N
    2. B.25N
    3. C.40N
    4. D.100N
    Show answer

    Answer: C. 40N

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  30. 30.

    A body of mass, M, moving with velocity, V, has a wavelength, X, associated with it. This phenomenon is called----------

    1. A.photoelectric effect
    2. B.heisenberg's uncertainty principle
    3. C.compton effect
    4. D.wave-particles paradox
    Show answer

    Answer: D. wave-particles paradox

    AI explanation

    1. Analyze the question A moving body of mass M and velocity V is said to have a wavelength X. This is the idea that matter (particles) can behave like waves. We need the name of this phenomenon.

    2. Explain the concept In 1924, Louis de Broglie proposed that every moving particle has a wave associated with it. Its wavelength is:

    λ = h / (M V)

    where h is Planck's constant (6.63 × 10⁻³⁴ J·s), M is the mass, and V is the velocity. This is called wave-particle duality (the "wave-particle paradox" in this question's wording), because matter shows both particle and wave properties.

    3. Check each option

    • A. Photoelectric effect: Electrons are ejected from a metal surface when light of sufficient frequency shines on it. It shows light behaving as particles (photons), not a wavelength for a moving mass.
    • B. Heisenberg's uncertainty principle: We cannot know a particle's exact position and momentum at the same time. It is not about a wavelength associated with a moving body.
    • C. Compton effect: X-rays scatter off electrons and lose energy, so their wavelength increases. It shows the particle nature of radiation.
    • D. Wave-particle paradox: A moving particle has a wavelength associated with it (de Broglie relation). This matches the question.

    4. Answer The correct option is D.

    5. Tip When you see "mass, velocity and wavelength" together, think de Broglie, λ = h/mv, which means wave-particle duality. Link the other options to their keywords:

    • photoelectric: electrons ejected by light
    • Compton: X-ray scattering
    • Heisenberg: position and momentum uncertainty

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  31. 31.

    The joule is equivalent to?

    1. A.Kg m2^{2} s−1^{-1}
    2. B.Kg2^{2} m s−2^{-2}
    3. C.Kg m2^{2} s−2^{-2}
    4. D.Kg m s−1^{-1}
    Show answer

    Answer: C. Kg m2^{2} s−2^{-2}

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  32. 32.

    In which of the following situations is friction not useful?

    1. A.Operation of a grinding machine
    2. B.Walking
    3. C.Application of brakes
    4. D.Moving piston in a sleeve
    Show answer

    Answer: D. Moving piston in a sleeve

    AI explanation

    Step 1: Analyze the question We need the situation where friction is not useful, meaning it is a nuisance, causing wear, heat and energy loss.

    Step 2: Concept Friction is the force that opposes relative motion between two surfaces in contact.

    • It is useful when we need grip, or when we need to slow something down or wear a surface away.
    • It is not useful when it causes unwanted wear, heat and energy loss between moving parts. In that case we reduce it with lubricants, ball bearings or polishing.

    Step 3: Check each option

    • A. Grinding machine: Friction between the grinding wheel and the material wears the material down. This is the whole purpose of grinding, so friction is useful.
    • B. Walking: Friction between the soles of our shoes and the ground gives grip. Without it we would slip, as on ice. Friction is useful.
    • C. Application of brakes: Friction between the brake pads and the wheel or drum slows the vehicle. Friction is useful.
    • D. Moving piston in a sleeve: A piston sliding in a cylinder or sleeve should move as freely as possible. Friction here causes wear, heat and loss of energy, which is why engines use lubricating oil. Friction is a nuisance, so it is not useful.

    Step 4: Answer The correct option is D.

    Tip: Ask whether the situation needs grip or stopping (friction useful: walking, brakes, grinding, striking a match) or smooth, continuous sliding (friction harmful: pistons, bearings, machine parts). In WASSCE, if you see moving machine parts, think "lubrication" and "friction is a disadvantage."

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  33. 33.

    The area under a force-time graph represents--------

    1. A.change in kinetic energy
    2. B.change in momentum
    3. C.change in work done
    4. D.change in internal energy
    Show answer

    Answer: B. change in momentum

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  34. 34.

    In a series R-L-C circuit at resonance, impedance is----

    1. A.maximum
    2. B.minimum
    3. C.capacitive
    4. D.inductive
    Show answer

    Answer: B. minimum

    AI explanation

    Analyze the question: We're asked what happens to the impedance of a series R-L-C circuit when it is at resonance.

    Concept: The impedance of a series R-L-C circuit is:

    Z = √[R² + (X_L − X_C)²]

    where X_L = ωL (inductive reactance) and X_C = 1/(ωC) (capacitive reactance).

    Solution:

    1. Resonance occurs when the inductive reactance equals the capacitive reactance: X_L = X_C.
    2. This gives X_L − X_C = 0.
    3. The impedance becomes Z = √(R² + 0) = R.
    4. Since the reactive part is zero, Z cannot get any smaller than R, so the impedance is at its minimum value.
    5. As a result, the current is at its maximum, since I = V/Z = V/R.
    6. The circuit behaves as a purely resistive circuit, so it is neither capacitive nor inductive. This rules out C and D.
    7. Option A is wrong because maximum impedance happens in a parallel LC circuit at resonance, not a series one.

    The resonant frequency is f₀ = 1/(2π√(LC)).

    Answer: The correct option is B. minimum.

    Exam tip: Remember "Series = Small impedance, Smax current". In a series resonance circuit, Z is minimum and I is maximum. In a parallel resonance circuit, it's the opposite: Z is maximum and I is minimum.

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

  36. 36.

    The length of a simple pendulum is increased by a factor of four. By what factor is its period increase?

    1. A.0.5π\pi
    2. B.2
    3. C.2π\pi
    4. D.4
    Show answer

    Answer: B. 2

    AI explanation

    Analyze the question: The length of a simple pendulum is multiplied by 4. We need to find how many times the period increases.

    Concept: The period of a simple pendulum is

    T = 2π√(L/g)

    So T is proportional to √L (g and 2π stay constant).

    Solution:

    • Original period: T₁ = 2π√(L/g)
    • New length: L₂ = 4L
    • New period: T₂ = 2π√(4L/g) = 2π × √4 × √(L/g) = 2 × 2π√(L/g)

    Therefore:

    T₂/T₁ = √4 = 2

    The period increases by a factor of 2.

    Checking the options:

    • A (0.5π) and C (2π) are wrong because π is already part of the formula and cancels out in the ratio.
    • D (4) would be correct only if T were directly proportional to L, but it depends on the square root of L.

    Tip: For a pendulum, T ∝ √L. Whatever factor you multiply the length by, take its square root to get the factor for the period. For example, if L is multiplied by 9, T is multiplied by 3. If L is multiplied by 4, T is multiplied by 2. The constants such as 2π and g cancel out in ratio questions, so you never need to include them in the final factor.

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  37. 37.

    Current is passed through two parallel conductors in the same direction. If the conductors are placed near each other, they will------------------

    1. A.move in a circle
    2. B.repel each other
    3. C.remain stationary
    4. D.attract each other
    Show answer

    Answer: D. attract each other

    AI explanation

    Analyze the question: Two parallel wires carry current in the same direction. What force acts between them?

    Concept: A current-carrying conductor produces a magnetic field around itself. When a second current-carrying conductor sits in that field, it experiences a force (F = BIL). This is the basis of the definition of the ampere.

    Rule for parallel conductors:

    • Currents in the same direction → the wires attract
    • Currents in opposite directions → the wires repel

    Step-by-step solution:

    1. Wire 1 carries current upward. By the right-hand grip rule, its magnetic field circles the wire. At the position of wire 2 (beside it), the field points into the page (say).
    2. Wire 2 also carries current upward, so it sits in the field of wire 1. Using Fleming's left-hand rule (First finger = field into the page, Second finger = current upward), the thumb (force) points toward wire 1.
    3. By the same reasoning, wire 1 experiences a force toward wire 2.
    4. The two forces point toward each other, so the wires attract.

    The magnitude of the force per unit length is:

    F/L = (μ₀ I₁ I₂) / (2πd)

    where d is the separation between the wires.

    Checking the options:

    • A. Move in a circle: no, the force is along the line joining them.
    • B. Repel: this happens only when currents are opposite.
    • C. Remain stationary: no, there is a net force.
    • D. Attract each other: correct.

    Answer: D. attract each other

    Exam tip: Remember "Same direction, Same side (attract); Opposite directions, Opposite motion (repel)." Note that this is the opposite of magnetic poles and electric charges, where like repels. For parallel currents, like currents attract.

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

  39. 39.

    The period of a 10 kHz radio wave traveling at 108^{8} ms−1^{-1} is--

    1. A.3.0 x 10−5^{-5}s
    2. B.1.0 x 10−4^{-4} s
    3. C.1.0 x 104^{4}s
    4. D.3.0 x 104^{4}s
    Show answer

    Answer: B. 1.0 x 10−4^{-4} s

    AI explanation

    Analyze the question: We are asked for the period of a radio wave with frequency 10 kHz. The wave speed (10⁸ m/s) is extra information, because the period depends only on frequency.

    Concept: Period and frequency are reciprocals:

    T = 1/f

    Solution:

    • f = 10 kHz = 10 × 10³ Hz = 10⁴ Hz
    • T = 1/f = 1/10⁴ = 1.0 × 10⁻⁴ s

    Check the options:

    • A (3.0 × 10⁻⁵ s) is wrong. It would come from using 3 × 10⁸ m/s in a wrong calculation, and it does not match 1/f.
    • B (1.0 × 10⁻⁴ s) matches our result.
    • C and D are far too large. A period of 10⁴ s would mean a very slow wave, not 10 kHz.

    Tip: Period questions often include distractors such as speed or wavelength. If you are given frequency and asked for period, just use T = 1/f. Also convert prefixes carefully: k = 10³, M = 10⁶. Speed matters only when you need wavelength (λ = v/f).

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  40. 40.

    In doping an intrinsic semiconductor to produce a p-type semiconductor,

    1. A.the semiconductor is heated up
    2. B.a donor element is added
    3. C.an acceptor element is added
    4. D.the semiconductor is conducted to a battery
    Show answer

    Answer: C. an acceptor element is added

    AI explanation

    Analyze the question: It asks what is done when doping an intrinsic semiconductor to make a p-type semiconductor.

    Concept:

    • An intrinsic semiconductor is pure (e.g., silicon or germanium, Group IV) with equal numbers of electrons and holes.
    • Doping means adding a small amount of impurity atoms to increase conductivity.
    • p-type: a trivalent impurity (Group III, e.g., boron, aluminium, gallium, indium) is added. Each impurity atom has only 3 valence electrons, so it leaves a missing electron (a hole) in a covalent bond. It readily accepts an electron, so it is called an acceptor. Holes become the majority carriers (p = positive).
    • n-type: a pentavalent impurity (Group V, e.g., phosphorus, arsenic, antimony) is added. It has 5 valence electrons, so it donates a free electron. It is called a donor, and electrons become the majority carriers.

    Solution:

    • A. Heating only produces more electron-hole pairs (thermal excitation). It is not doping and does not make the material p-type.
    • B. A donor element produces an n-type semiconductor, so this is wrong.
    • C. An acceptor element (trivalent) creates holes, giving a p-type semiconductor. This is correct.
    • D. Connecting to a battery is biasing, not doping.

    Answer: C. an acceptor element is added

    Tip: Remember "P-type = Positive holes = Acceptor (Group III, 3 valence electrons)", and "N-type = Negative electrons = Donor (Group V)". Pair them as Acceptor → p, Donor → n.

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  41. 41.

    The basic principle of operation of a beam balance is------------------

    1. A.Hooke's law
    2. B.Archimedes principle
    3. C.law of flotation
    4. D.principle of moments
    Show answer

    Answer: D. principle of moments

    AI explanation

    Step 1: Analyze the question We need the basic principle behind how a beam balance works. A beam balance has a horizontal beam pivoted at its centre (the fulcrum), with a pan on each side. One pan holds the object and the other holds known masses.

    Step 2: Explain the concept The principle of moments says that when a body is in rotational equilibrium, the sum of the clockwise moments about the pivot equals the sum of the anticlockwise moments about the same pivot.

    Moment = force × perpendicular distance from the pivot

    Step 3: Apply it to the beam balance

    • The two pans hang at equal distances (d) from the pivot.
    • The object has weight W₁ = m₁g, and the standard masses have weight W₂ = m₂g.
    • The beam balances (stays horizontal) when:

    Clockwise moment = Anticlockwise moment m₁g × d = m₂g × d so m₁ = m₂

    When the beam is balanced, the unknown mass equals the known mass. This is the principle of moments in action.

    Step 4: Check the other options

    • A. Hooke's law: applies to springs (extension is proportional to load), as in a spring balance, not a beam balance.
    • B. Archimedes' principle: deals with upthrust on bodies in fluids (hydrometers, floating bodies).
    • C. Law of flotation: a floating body displaces its own weight of fluid (ships, hydrometers).
    • D. Principle of moments: correct, as shown above.

    Step 5: Answer The correct option is D. principle of moments.

    Exam tip: Match the instrument to its law:

    • Beam balance, see-saw, lever: moments
    • Spring balance: Hooke's law
    • Hydrometer, ships: flotation/Archimedes

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  42. 42.

    A lamp is rated 240 V, 60 W. Determine the resistance of the lamp when lit?

    1. A.120Ω\Omega
    2. B.240Ω\Omega
    3. C.540Ω\Omega
    4. D.960Ω\Omega
    Show answer

    Answer: D. 960Ω\Omega

    AI explanation

    Analyze the question: A lamp has a rating of 240 V and 60 W. We need its resistance when it is operating normally (lit). Concept: Electrical power is related to voltage and resistance by: P = V²/R, so R = V²/P This comes from combining P = IV with Ohm's law, V = IR. Solution: R = V²/P = (240)² / 60 R = 57,600 / 60 R = 960 Ω Check using current: I = P/V = 60/240 = 0.25 A R = V/I = 240/0.25 = 960 Ω ✓ Answer: The resistance of the lamp when lit is 960 Ω, which is option D. Tip: When a question gives a rating like "V volts, P watts", go straight to R = V²/P. Be careful not to just divide V by P or confuse the numbers. Also remember that a lamp's resistance when lit (hot filament) is higher than when cold.

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  43. 43.

    The linear expansivity, α\alpha, and cubic expansivity, γ\gamma, of a material are related by the equation?

    1. A.γ\gamma=a
    2. B.γ\gamma=3α\alpha
    3. C.γ\gamma=2a
    4. D.γ\gamma=13α\frac{1}{3} \alpha
    Show answer

    Answer: B. γ\gamma=3α\alpha

    AI explanation

    Analyze the question: It asks for the relationship between linear expansivity (α) and cubic (volume) expansivity (γ) for a solid material.

    Concept: When a solid is heated, each of its dimensions expands. Linear expansivity α is the fractional increase in length per unit rise in temperature. Cubic expansivity γ is the fractional increase in volume per unit rise in temperature.

    Derivation:

    Take a cube of side L₀ at the starting temperature, so its volume is V₀ = L₀³.

    After a temperature rise Δθ, the new side is:

    L = L₀(1 + αΔθ)

    The new volume is:

    V = L³ = L₀³(1 + αΔθ)³

    Expanding with the binomial theorem:

    V = V₀(1 + 3αΔθ + 3α²Δθ² + α³Δθ³)

    Because α is very small (about 10⁻⁵ per K), the terms α² and α³ are negligible, so:

    V ≈ V₀(1 + 3αΔθ)

    Compare this with the definition V = V₀(1 + γΔθ):

    γ = 3α

    Checking the options:

    • A. γ = α is wrong.
    • B. γ = 3α is correct.
    • C. γ = 2α would be the areal expansivity relation (β = 2α), so it is wrong.
    • D. γ = α/3 is wrong.

    Tip: Remember the pattern α : β : γ = 1 : 2 : 3. Linear is 1D, area is 2D, volume is 3D, so the multiplier equals the number of dimensions.

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  44. 44.

    Which of the folowing statements about light travelling from one material medium to another is not correct?

    1. A.The refracted angle is less than the incident angle if the speed is higher in the first material
    2. B.Its wavelength does not change
    3. C.It bends away from the normal if the speed is lower in the first material
    4. D.Its frequency changes.
    Show answer

    Answer: C. It bends away from the normal if the speed is lower in the first material

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  45. 45.

    The half-life of a radioactive substance is 15 hours. If at some instance, the sample has a mass of 512 g, calculate the time it will take 78\frac{7}{8} of the sample to decay

    1. A.15 hours
    2. B.30 hours
    3. C.45 hours
    4. D.60 hours
    Show answer

    Answer: C. 45 hours

    AI explanation

    Analyze the question: The half-life is 15 hours. We need the time for 7/8 of the sample to decay, which means 1/8 of the sample remains.

    Concept: After each half-life, the remaining mass is halved:

    N = N₀ × (1/2)ⁿ, where n = t / T½

    Solution:

    • Fraction remaining = 1 − 7/8 = 1/8
    • (1/2)ⁿ = 1/8 = (1/2)³, so n = 3
    • t = n × T½ = 3 × 15 = 45 hours

    Check with the mass (512 g):

    • After 15 h: 256 g
    • After 30 h: 128 g
    • After 45 h: 64 g

    The decayed mass is 512 − 64 = 448 g, and 448/512 = 7/8. ✔

    Answer: C. 45 hours

    Tip: When a question says a fraction "has decayed," always subtract it from 1 to get the fraction remaining. Then write that remainder as a power of ½ (1/2, 1/4, 1/8, 1/16, ...). The power is the number of half-lives. The mass given (512 g) is not needed here, since only the fraction matters.

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  46. 46.

    The power of the lens is +2.5D. What is the radius of the curvature?

    1. A.2.5 cm
    2. B.25.0 cm
    3. C.40.0 cm
    4. D.80.0 cm
    Show answer

    Answer: D. 80.0 cm

    AI explanation

    The question is incomplete as written, so we need to identify what kind of lens it describes. The options suggest a standard WASSCE-style question: the power of a lens is +2.5 D, and we need the radius of curvature. Let's work it out.

    Step 1: Concept Power of a lens: P = 1/f (f in metres)

    The focal length and radius of curvature are related by:

    • For a spherical mirror: R = 2f
    • For a thin lens with equal curvature, the lensmaker's formula applies.

    Step 2: Focal length f = 1/P = 1/2.5 = 0.4 m = 40 cm

    Step 3: Radius of curvature This question is most likely from a version about a concave/convex mirror or a lens treated with R = 2f:

    R = 2f = 2 × 40 = 80 cm

    Check with the lensmaker's formula: For a glass lens with refractive index n = 1.5 and equal curvature (biconvex), 1/f = (n−1)(2/R), so R = 2(n−1)f = 2(0.5)(40) = 40 cm. This would give option C. However, the question gives no refractive index, so the intended approach is the simple R = 2f relationship.

    Step 4: Answer Using f = 40 cm and R = 2f, we get R = 80 cm, which is option D.

    Note: The question as printed doesn't mention a refractive index, so the R = 2f relationship is the one the examiners intend. If a refractive index were given, you would use the lensmaker's formula instead.

    Tip: Always convert power to focal length first: f = 1/P in metres. Then, if no refractive index is given, use R = 2f. Remember that dioptres need metres, so convert your final answer to centimetres.

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  47. 47.

    A small object of mass 50 g is released from a point A. Determine the velocity of the object when it reaches a point B, a vertical distance of 30m below A. [g = 10 ms−2^{-2}

    1. A.1.5 ms−1^{-1}
    2. B.6.0 m s−1^{-1}
    3. C.17.3 m s−1^{-1}
    4. D.24.5 m s−1^{-1}
    Show answer

    Answer: D. 24.5 m s−1^{-1}

    AI explanation

    Analyze the question: An object is released (so it starts from rest) and falls a vertical distance of 30 m. We need its speed at B. The mass (50 g) is not needed, because in free fall the speed does not depend on mass. Concept: Use conservation of energy (loss in potential energy = gain in kinetic energy), or equivalently the equation of motion v² = u² + 2gh. Solution: mgh = ½mv², so v² = 2gh (the mass cancels) With u = 0, g = 10 m/s² and h = 30 m: v² = 2 × 10 × 30 = 600 v = √600 ≈ 24.5 m/s Check against the options: √600 = 10√6 ≈ 10 × 2.449 = 24.5 m/s, which matches option D. (Option C, 17.3, is √300, which would come from forgetting the factor of 2.) Tip: In "released from rest" problems, the mass is usually a distractor. Go straight to v = √(2gh). Also remember that forgetting the "2" gives the common wrong option (here C).

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  48. 48.

    From the principle of flotation, a body sinks in a fluid until it displace a quantity equal to its own?

    1. A.density
    2. B.mass
    3. C.weight
    4. D.volume
    Show answer

    Answer: C. weight

    AI explanation

    Analyze the question: It asks what quantity of fluid a floating body displaces, according to the principle of flotation.

    Concept: The law of flotation says that a floating body displaces a weight of fluid equal to its own weight. It comes from Archimedes' principle, which says the upthrust on a body equals the weight of the fluid it displaces.

    Step-by-step solution:

    1. A body floats when it is in equilibrium. This means the upward force (upthrust) balances the downward force (the body's weight).
    2. Upthrust = weight of fluid displaced.
    3. For equilibrium, weight of body = upthrust.
    4. Therefore, weight of body = weight of fluid displaced.

    About the options:

    • Density: Not a quantity that can be "displaced," so this is wrong.
    • Mass: Mass of fluid displaced does equal the body's mass, since g cancels. This is true, but the principle is traditionally stated in terms of weight.
    • Volume: The volume displaced equals the body's volume only when it is fully submerged. A floating body displaces less volume than its own, so this is wrong.

    Answer: C. weight

    Tip: Remember "Floating means weight equals weight," that is, the weight of the body equals the weight of the fluid displaced. In WASSCE, when both mass and weight appear as options, choose weight, because the principle is a statement about forces.

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  49. 49.

    Using venier calipers, which of the following readings gives the correct measurement for the length of a rod?

    1. A.4.1 cm
    2. B.4.13cm
    3. C.125 cm
    4. D.1254 cm
    Show answer

    Answer: B. 4.13cm

    AI explanation

    Analyze the question

    The question asks which reading is a valid measurement from a vernier caliper. The key is the precision (least count) of the instrument.

    Concept

    A standard vernier caliper has:

    • Main scale divisions of 1 mm (0.1 cm)
    • A vernier scale with 10 divisions, giving a least count of 0.1 mm = 0.01 cm

    So a reading from a vernier caliper is recorded to two decimal places in centimetres (the nearest 0.01 cm).

    Reading = main scale reading + (vernier division coinciding × 0.01 cm)

    Solution

    Check each option:

    • A. 4.1 cm – only one decimal place. This is the precision of a plain ruler (nearest mm), not a vernier caliper. It doesn't show the vernier contribution.
    • B. 4.13 cm – two decimal places (main scale 4.1 cm + vernier 3 × 0.01 cm). This matches the precision of a vernier caliper. ✔
    • C. 125 cm – no decimal places, and far too long. Vernier calipers measure small lengths (typically up to about 15 cm). ✘
    • D. 1254 cm – about 12.5 m, impossible for a vernier caliper and has no decimal precision. ✘

    Answer

    The correct option is B (4.13 cm).

    Tip

    For vernier calipers, remember: cm readings with 2 decimal places (or mm readings with 1 decimal place). For a micrometer screw gauge, the reading is usually in mm with 2 decimal places (e.g., 4.13 mm). Always check the least count first and make sure your answer matches that precision.

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  50. 50.

    The magnetic material produced from the chemical combination of metal oxides and has a very high resistance to electric current is called

    1. A.ferrite substance
    2. B.paramagnetic substance
    3. C.ferromagnetic substance
    4. D.diamagnetic substance
    Show answer

    Answer: A. ferrite substance

    AI explanation

    Analyze the question: We need a magnetic material that is made by chemically combining metal oxides and that has very high electrical resistance.

    Concept: Ferrites are ceramic-like compounds made from iron(III) oxide (Fe₂O₃) combined with oxides of other metals such as manganese, zinc, nickel, or barium. They are ferrimagnetic. Because they are oxide compounds, they are poor electrical conductors, which gives them very high resistivity.

    Why this matters: The high resistivity means very small eddy currents are induced in them. That is why ferrites are used in:

    • transformer cores for high-frequency use
    • radio antennas (ferrite rods)
    • computer memory cores
    • magnetic tapes

    Checking each option:

    • A. Ferrite substance: It is made from metal oxides and has very high resistivity. This matches the description.
    • B. Paramagnetic substance: These are weakly attracted by a magnetic field (e.g., aluminium, platinum). The term describes magnetic behaviour, not a metal-oxide compound with high resistance.
    • C. Ferromagnetic substance: These are strongly magnetic metals such as iron, cobalt, and nickel. They are good conductors, so they do not match "high resistance."
    • D. Diamagnetic substance: These are weakly repelled by a magnetic field (e.g., copper, bismuth, water). They do not match the description.

    Answer: A (ferrite substance)

    Exam tip: Remember "Ferrite = Ferric oxide + other metal oxides = High resistance." If you see "oxides" and "high resistance" together in a magnetism question, think ferrite.

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