All 50 questions from the West African Examinations Council (WAEC) Physics 2015 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
Which of the following statements about mass and weight are correct? I. Weight is the force of gravity on a body II. The mass of a body is the quantity of matter in the body III. The weight of a body is greatest at the equator IV. The mass of a body is greatest at the poles.
A. I and II onlyCorrect
B. I and III only
C. II and IV only
D. III and IV only
Explanation
Weight is the force of gravity on a body (I is correct) and mass is the quantity of matter in a body (II is correct). Weight is actually greatest at the poles (not the equator) and mass does not depend on location, so III and IV are false.
The barometric reading at a place is 73.5 cm Hg. Calculate the pressure at a point 30 m below the surface of water contained in a reservoir at the place. [g = 10 ms⁻², density of mercury 13.6×10⁴ kg m⁻³, density of water = 1.0×10³ kg m⁻³]
A. 4.0×10⁵Nm⁻²Correct
B. 3.0×10⁵Nm⁻²
C. 2.0×10⁵Nm⁻²
D. 1.0×10⁵Nm⁻²
Explanation
Converting the barometer reading to Pascals gives about 1.0×10⁵ N/m². Adding the pressure due to the 30 m water column (ρgh = 1000×10×30 = 3×10⁵ N/m²) gives a total pressure of about 4.0×10⁵ N/m².
A body is projected with an initial velocity u at an angle θ to the horizontal. The time taken by it to reach its maximum height is given by the expression
A. 2u sinθ/g
B. u² sin²θ/2g
C. u sinθ/gCorrect
D. u sinθ/2g
Explanation
At maximum height the vertical velocity is zero. Using v = u sinθ − gt with v = 0 gives t = u sinθ/g.
Which of the following statements describes a body in a stable equilibrium correctly?
A. a person walking on a tight-rope
B. a ball on a smooth horizontal table
C. a ball resting on an inverted hemispherical bowl
D. a ball in the middle of a hemispherical bowlCorrect
Explanation
A body is in stable equilibrium if, when slightly displaced, it returns to its original position; a ball resting in the middle of a hemispherical bowl (low centre of gravity, wide base of support) is a classic example.
In a school compound, a girl walks 40 m due east from the laboratory to the staff room to submit her report. Then she turns and walks 30 m due north to her classroom. Determine the magnitude of her displacement from the laboratory.
A. 10 m
B. 35 m
C. 50 mCorrect
D. 70 m
Explanation
By Pythagoras' theorem, displacement = √(40² + 30²) = √2500 = 50 m.
Two strings each inclined at an angle of 30° to the horizontal are used to hold a bucket of water weighing 20 N. Calculate the tension in each string.
A. 20√3 N
B. 20 NCorrect
C. 10√3 N
D. 10 N
Explanation
By symmetry, the two equal tensions each make 60° with the horizontal (30° with the vertical each side), and applying the sine rule/resolving forces gives T₁ = T₂ = 20 N.
A bullet fired vertically upwards reaches a height of 500 m. Neglecting air resistance, calculate the magnitude of the initial velocity of the bullet. [g = 10 ms⁻²]
A. 500.0 ms⁻¹
B. 100.0 ms⁻¹Correct
C. 70.0 ms⁻¹
D. 50.0ms⁻¹
Explanation
At maximum height v = 0, so from v² = u² − 2gh: 0 = u² − 2(10)(500), giving u² = 10000 and u = 100.0 ms⁻¹.
A body of mass 1000 kg is released from a height of 10 m above the ground. Determine its kinetic energy just before it strikes the ground. [g = 10 ms⁻²]
A. 10 J
B. 10³ J
C. 10⁴ J
D. 10⁵ JCorrect
Explanation
By conservation of energy, KE just before impact = initial PE = mgh = 1000×10×10 = 100,000 J = 10⁵ J.
The diagrams below illustrate four test-tubes containing the same volume of a liquid at different pressures. In which of the test-tubes does the liquid boil last if they are supplied with the same quantity of heat?
A. the tube at 2 atmospheresCorrect
B. the tube at 1½ atmosphere
C. the tube at 1 atmosphere
D. the tube at less than 1 atmosphere
Explanation
An increase in pressure raises the boiling point of a liquid, so the test-tube under the highest pressure (2 atmospheres) requires the highest temperature and therefore boils last.
The diagram above illustrates a block and tackle pulley system in which an effort E supports a load of 100.0 N. If the efficiency of the machine is 75%, calculate the value of E.
A. 22.2 NCorrect
B. 38.0 N
C. 67.0 N
D. 75.0 N
Explanation
With a velocity ratio of 6 (six pulleys), MA = Load/Effort and Efficiency = (MA/VR)×100%. So Effort = Load/(Efficiency×VR) = 100/(0.75×6) = 22.2 N.
A quantity of hot water at 100°C is added to 400 g of water at 10°C until the temperature of the mixture is 60°C. Calculate the mass of the hot water added. [Specific heat capacity of water = 4200 J kg⁻¹K⁻¹]
A. 200 g
B. 320 g
C. 400 g
D. 500 gCorrect
Explanation
Heat lost by hot water = heat gained by cold water: M(4200)(100−60) = 0.4(4200)(60−10), giving M = (0.4×50)/40 = 0.5 kg = 500 g.
In an experiment in which a molten substance is allowed to cool, the cooling curve shown above was obtained. The temperature 60°C is known as the
A. vaporization point
B. cooling temperature
C. boiling point
D. melting pointCorrect
Explanation
The flat (plateau) section of a cooling curve marks the temperature at which the substance changes from liquid to solid at a constant temperature - the melting (freezing) point.
An object is placed 15 cm from a diverging lens of focal length 12 cm. The image of the object formed by the lens is
A. real and 6.67 cm from the lens
B. virtual and 6.67 cm from the lensCorrect
C. real and 60.00 cm from the lens
D. virtual and 60.00 cm from the lens
Explanation
Using 1/v = 1/u − 1/f with f = −12 cm (diverging) and u = 15 cm gives v ≈ −6.67 cm; the negative sign shows the image is virtual, located 6.67 cm from the lens.
Which of the following types of lenses is suitable for correcting the eye defect illustrated by the ray diagram above (converging rays that focus behind the retina)?
A. Bi-convergingCorrect
B. Bi-diverging
C. Piano diverging
D. Diverging meniscus
Explanation
The ray diagram illustrates hypermetropia (long-sightedness), where the image forms behind the retina; it is corrected using a converging (convex) lens.
A girl standing some distance from the foot of a tall cliff claps her hands and hears the echo 0.8 s later. Calculate her distance from the cliff. [Speed of sound in air = 320 ms⁻¹]
A. 82 m
B. 102 m
C. 128 mCorrect
D. 140 m
Explanation
Distance = (speed × time)/2 = (320×0.8)/2 = 128 m.
Red light travels faster than blue light when both of them pass through a glass prism because the
A. refractive index of red light is greater than that of blue light
B. refractive index of blue light is greater than that of red lightCorrect
C. red light is more intense than the blue light
D. blue light is more intense than the red light
Explanation
Blue light is refracted (bent) more and travels slower in glass, meaning it has a higher refractive index than red light, which travels faster with a lower refractive index.
All electromagnetic waves in a vacuum have the same
A. wavelength
B. frequency
C. speedCorrect
D. amplitude
Explanation
All electromagnetic waves travel at the same speed in a vacuum (the speed of light, c), though their wavelengths, frequencies and amplitudes may differ.
An alternating current supply is connected to an electric lamp which lights with the same brightness as it does with a direct current source of e.m.f. 6 V. The peak potential difference of the a.c. supply is
A. 4.6 V
B. 6.0 V
C. 8.5 VCorrect
D. 12.0 V
Explanation
Peak voltage = rms voltage × √2 = 6×1.414 ≈ 8.5 V.
Which of the following statement(s) about a three-pin plug is/are correct? I. The brown wire is the live wire II. The fuse is connected to the live wire III. The earth wire is coloured blue
A. I only
B. II only
C. I and II onlyCorrect
D. I, II and III
Explanation
The brown wire is live and the fuse is connected to the live wire (I and II correct); the earth wire is green/yellow, not blue (III is false - blue is the neutral wire).
The mass of the earth is 6.0×10²⁴ kg and that of the moon is 7.0×10²² kg. If the distance between them is 4.0×10⁸ m, calculate the force of attraction between them. [G = 6.7×10⁻¹¹ Nm²kg⁻²]
A. 1.8×10¹² N
B. 1.8×10¹⁵ N
C. 1.8×10¹⁸ N
D. 1.8×10²⁰ NCorrect
Explanation
F = GMm/r² = (6.7×10⁻¹¹×6×10²⁴×7×10²²)/(4×10⁸)² ≈ 1.8×10²⁰ N.
When current flows through a moving-coil galvanometer, the force exerted on the pointer depends on the: I. strength of the current; II. magnetic field strength; III. length of the coil. Which of the statement(s) above is/are correct?
A. I only
B. II only
C. I and III only
D. I, II and IIICorrect
Explanation
The deflecting force/torque on the coil depends on the current strength, the magnetic field strength, and the length (and other dimensions) of the coil, so all three (I, II and III) are correct.
²²⁶Ra emits two alpha particles to produce Polonium (Po) nuclide. The correct formula for the nuclide is
A. ²²⁴₈₆Po
B. ²²²₈₆Po
C. ²²²₈₄Po
D. ²¹⁸₈₄PoCorrect
Explanation
Each alpha particle reduces the mass number by 4 and the atomic number by 2. Two alpha particles: mass number 226−8=218, atomic number 88−4=84, giving ²¹⁸₈₄Po.
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