All 50 questions from the West African Examinations Council (WAEC) Physics 2021 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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1. Which of the following quantities is not an example of force?
Mass is not a force; it is the quantity of matter contained in a body. Tension, weight and friction are all forces.
2. The reason for laminating the soft iron core of a transformer is to
Laminating the core breaks up the paths for induced (eddy) currents, reducing energy loss due to eddy currents.
3. Formation of hydrogen bubbles at the copper plate of a primary cell is called
This defect, where hydrogen gas collects on the copper plate and increases internal resistance, is called polarization.
4. Which of the following factors does not affect the rate of evaporation of a liquid?
Evaporation rate depends on temperature, surface area, wind speed and the nature of the liquid — not on its volume.
5. The opening in the eye through which light passes to the retina is called the
The pupil is the opening (controlled by the iris) that allows light to enter and reach the retina.
6. A heat sensitive resistor made of a semiconductor is called a
A thermistor is a semiconductor resistor whose resistance changes significantly with temperature.
7. Electric motor primarily converts
An electric motor's main function is converting electrical energy into mechanical (kinetic) energy.
8. Which of the following statements about the molecules of solids and liquids is correct?
Molecules in both solids and liquids are closely packed and vibrate about relatively fixed positions (more freely in liquids).
9. The distance between a node and its adjacent antinode of a transverse wave is equal to
Node-to-node or antinode-to-antinode distance is λ/2, so node-to-adjacent-antinode distance is λ/4.
10. Which of the following sketched graphs below illustrates the correct variation of the gravitational force, Fg, between two objects and the distance, d, between their centres?
Gravitational force follows an inverse-square law (Fg∝1/d²), giving a curve that falls steeply and approaches zero — the shape shown in graph B.
11. Which of the following actions will increase the capacitance of a parallel plate capacitor? I. Decreasing the distance between the plates II. Increasing the distance between the plates III. Increasing the area of the plates overlap IV. Avoiding the use of dielectric between the plates
Capacitance C=ε₀εrA/d increases when plate separation (d) decreases and when overlapping plate area (A) increases — statements I and III.
12. A metallic sphere is heated from 27°C to 200°C without change of state. Which of the following changes would have resulted from the heating?
Heating expands the metal (volume increases). Since density=mass/volume and mass stays constant, density decreases.
13. The acceleration of a moving object can be determined from the
Acceleration is the rate of change of velocity, given by the slope (gradient) of a velocity-time graph.
14. A student wishes to measure the potential difference across a resistor, R. She has a galvanometer, G and some connecting wires, what else does she need?
To convert a galvanometer into a voltmeter, a high resistance (multiplier) is connected in series with it.
15. The handle of a screw jack is 35 cm long and the pitch of the screw is 0.5 cm. What force must be applied at the end of the handle to lift a load of 2000 N if the efficiency of the jack is 30%? [π=22/7]
Velocity ratio = 2πa/p = 2π(35)/0.5 = 440. Mechanical advantage = efficiency×VR = 0.3×440 = 132. Effort = Load/M.A. = 2000/132 ≈ 15.2 N.
16. The inductive reactance in a circuit of frequency 100 Hz is 1 Ω. Calculate the inductance of the inductor. [π=3.14]
XL=2πfL → L=XL/(2πf)=1/(2×3.14×100)=1.59×10⁻³ H.
17. The diagram above illustrates the velocity-time graph of a body. Calculate the distance covered by the body during the motion.
Distance = area under the graph = rectangle(0-4s)+trapezium(4-12s) = (4×4) + ½(4+10)×8 = 16+56 = 72 m.
18. An atom that emits an α-particle
Alpha decay reduces the proton number by 2, changing the atom into a daughter of a different element.
19. Which of the following units is equivalent to the unit of electric current?
Current I=Q/t, so its unit is coulombs per second (C s⁻¹), which is the ampere.
20. A ball is swung in a horizontal circle of centre O with a constant speed. What is the direction of its acceleration?
Circular motion at constant speed has centripetal acceleration directed toward the centre, O.
21. Which of the following statements is an effect of compressing gas molecules at constant temperature?
Compressing the gas reduces its volume, so molecules collide with the container walls more frequently, increasing pressure.
22. The diagram above is an illustration of an a.c. circuit. Calculate the reactance of the capacitor.
Xc=1/(2πfC). With f=500/π Hz and C=5µF: Xc=1/(2π×(500/π)×5×10⁻⁶)=10⁶/5000=200 Ω.
23. A current of 2 A passes through a wire of resistance 4 Ω for 3 minutes. Calculate the energy lost.
Energy = I²Rt = 2²×4×(3×60) = 4×4×180 = 2880 J.
24. Which of the following statements about the universal gravitational constant, G, is true?
From F=Gm₁m₂/r², G=Fr²/m₁m₂, giving SI unit Nm²kg⁻² and dimensions M⁻¹L³T⁻².
25. The sketched graph above represents a progressive wave moving from left to right. The period of the wave is 0.125 s. Determine the values of the amplitude and wavelength respectively of the wave.
Amplitude = half the peak-to-peak height = 16/2 = 8 cm. The 27 cm shown spans 3 wavelengths, so wavelength = 27/3 = 9 cm.
26. Determine the speed of the wave.
Speed v=fλ=λ/T=9/0.125=72 cm s⁻¹.
27. Which of the following curved surfaces will produce a real image? I. Concave mirror II. Convex mirror III. Diverging lens IV. Converging lens
A convex mirror and a diverging lens always form virtual images, so real images can only come from a concave mirror and a converging lens under suitable conditions.
28. The components of vectors Q and R are (-3.0,5.5) and (9.2,4.4), respectively. Determine the components of Q+R.
Adding component-wise: Q+R = (-3.0+9.2, 5.5+4.4) = (6.2, 9.9).
29. Which of the following arrangements of radiations below shows decreasing order of wavelengths?
In the electromagnetic spectrum, radio waves have the longest wavelength, followed by infrared, then X-rays with the shortest.
30. An electric pressing iron is connected to the mains using an insulated wire. After some minutes, the wire becomes very hot. The heat generated in the wire can be minimized by replacing the wire with one of
A thicker wire (greater diameter) has lower resistance (R=ρl/A), reducing the heating effect (H=I²Rt) for the same current.
31. In the diagram above, a bulb is lit by drawing 2.0 A from 440 V a.c. source. Calculate the cost of keeping the bulb on for two days at $0.40 per kilowatt-hour.
Power=VI=440×2=880W=0.88kW. Energy in 2 days (48h)=0.88×48=42.24 kWh. Cost=42.24×0.40 ≈ $16.90.
32. A wire of cross-sectional area 2π×10⁻⁸ m and resistivity 1.1×10⁻⁸ Ωm has a resistance of 21 Ω. Calculate the length of the wire. [π=22/7]
R=ρl/A → l=RA/ρ = (21×2π×10⁻⁸)/(1.1×10⁻⁸) ≈ 120 m.
33. Which of the following statements best describes the particles in a solid at room temperature?
In a solid, particles are closely packed in a fixed arrangement but vibrate about their mean positions.
34. Aman weighing 200 N runs up a staircase in 5 s. If the height of the staircase is 9 m, calculate the power of the man.
Power = Work/time = (Weight×height)/time = (200×9)/5 = 360 W.
35. A rotating disc contains a set of holes in a circle. An air jet is directed onto the holes and a note of frequency 480 Hz is produced. If the number of holes is 20, calculate the speed of rotation of the disc.
Frequency = (revolutions/s) × (holes). So rev/s = 480/20 = 24 revs/s.
36. A force of 10 N, acting continuously, increases the kinetic energy of an object from 20 J to 60 J. Find the distance moved by the object.
Work done = ΔKE = 60-20 = 40 J = Force×distance. Distance = 40/10 = 4 m.
37. An electric circuit consists of a resistor, a battery and a key. If the voltage of the battery is increased, there would be an increase in the
Increasing the voltage increases the current flowing (V=IR), and the greater current raises the temperature of the resistor due to increased heating effect.
38. A radioactive material has a half-life of 1.0 hour. If 200.0 g of it was present at 6 a.m. on a certain day, how many grams will have decayed by 9 a.m. on the same day?
From 6 a.m. to 9 a.m. is 3 hours = 3 half-lives. 200→100→50→25 g remaining. Decayed = 200-25 = 175.0 g.
39. Which of the following statements about a loudspeaker is correct except that
In a loudspeaker, the current in the speech coil alternates, so the resulting magnetic force is NOT uni-directional — making this statement the incorrect one.
40. An ice cube has a mass of 20 g at 5 °C. Calculate the energy required to raise its temperature to 0 °C. [Specific heat capacity of ice = 2.1 J g⁻¹ °C⁻¹]
Energy = mcΔθ = 20×2.1×(5-0) = 210 J.
41. A stone is thrown horizontally with an initial velocity of 15 ms⁻¹ from a tower 20 m high. How long does it take to reach the ground? [g=10 ms⁻²]
Using s=ut+½gt² for the vertical motion (u=0 vertically): 20=½×10×t² → t²=4 → t=2 s.
42. Which of the following statements is not a characteristic of a plane progressive wave?
In a progressive wave, all points have the same amplitude; only the phase differs along the profile, so 'different amplitudes' is not a characteristic.
43. The electrons in a cathode-ray tube are produced by
Electrons are produced by thermionic emission — heating a metal filament (the cathode) until electrons are emitted.
44. Which of the following statements about distance and displacement is not correct?
Distance is a scalar quantity (only magnitude); displacement is the vector quantity, not distance.
45. A note produced by an instrument is distinguished from a similar note produced by another instrument by the
Two notes of the same pitch and loudness from different instruments differ in their overtone content, giving each instrument its characteristic timbre (quality).
46. According to Pascal's principle, the pressure in a fluid is always
Pascal's principle states that pressure applied to an enclosed fluid is transmitted equally in all directions throughout the fluid.
47. Which of the following set of quantities have all members which are all vectors?
Force, displacement and momentum are all vector quantities (each has magnitude and direction); the other sets each include a scalar.
48. If the relative humidity of the atmosphere increases, the rate of evaporation of sweat from the human body
Higher relative humidity means the air already holds more moisture, so it absorbs sweat vapour more slowly — the evaporation rate decreases.
49. Which of the following factors is not among those that determine the resistance of a wire?
Resistance R=ρl/A depends on the wire's length, cross-sectional area and resistivity (material) — not directly on its mass.
50. Which of the following scientists suggested that moving particles exhibit wave properties?
Louis de Broglie proposed the wave-particle duality of matter, suggesting that moving particles (like electrons) also exhibit wave properties.
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