47 questions. Try each one, then open the answer to check yourself and read the explanation.
What is the reading of the vernier calipers shown above?
Answer: C (1.39cm)
The vernier zero lies just short of the 1.4 cm mark (main scale 1.3 cm), and the 9th vernier line lines up with a main-scale line, so the reading is 1.3 + 0.09 = 1.39 cm.
A boat travels due east at a speed of 40 m s−1 across a river flowing due south at 30 m s−1. What is the resultant speed of the boat?
Answer: C (50.0 m s−1)
The two velocities are at right angles: resultant = √(402 + 302) = √2500 = 50.0 m s−1.
An object is projected with a velocity of 80 m s−1 at an angle of 30° to the horizontal. The maximum height reached is
Answer: B (80m)
H = u2 sin2θ / 2g = 802 × (0.5)2 ÷ 20 = 1600 ÷ 20 = 80 m (g = 10 m s−2).
A motor vehicle is brought to rest from a speed of 15 m s−1 in 20 seconds. Calculate the retardation.
Answer: A (0.75 m s−2)
Retardation = change in velocity ÷ time = 15 ÷ 20 = 0.75 m s−2.
Which of the following is TRUE of a particle moving in a horizontal circle with constant angular velocity?
Answer: A (The energy is constant but the linear momentum varies)
The speed is constant, so the kinetic energy is constant, but the direction of motion keeps changing, so the velocity and the momentum (mv) keep changing.
A stone thrown vertically upwards returns to the ground. Which of the following figures represents the velocity-time graph?
Answer: D (Figure D)
Velocity starts positive (upwards), falls at a steady rate g to zero at the top, then becomes negative (downwards) as the stone falls: one straight line crossing the time axis, as in D.
The diagram above shows a uniform wood of weight 200 N and length 50m. It is pivoted at one end and suspended by a cord at the other end at an angle of 30° to the wood. Calculate the tension in the cord if the wood is horizontal.
Answer: D (200 N)
Moments about the pivot: 200 × 25 = T sin 30° × 50, so 5000 = 25T and T = 200 N.
An object of mass 50kg is released from a height of 2m. Find the kinetic energy just before it strikes the ground.
Answer: B (1000 J)
The potential energy lost becomes kinetic energy: mgh = 50 × 10 × 2 = 1000 J.
A cone in an unstable equilibrium has its potential energy
Answer: A (decreased)
A cone balanced on its tip is in unstable equilibrium: any small tilt lowers its centre of gravity, so its potential energy decreases and it falls over.
Calculate the magnitude of the force required to just move a 20kg object along a horizontal surface if the coefficient of friction is 0.2 (g = 10 m s−2)
Answer: B (40.0 N)
F = μR = μmg = 0.2 × 20 × 10 = 40.0 N.
Calculate the velocity ratio of a screw jack of pitch 0.3cm if the length of the tommy bar is 21cm.
Answer: D (140π)
V.R. = 2πL ÷ pitch = 2π × 21 ÷ 0.3 = 140π.
Which of the following graphs correctly represents the relationship between the load and the velocity ratio of a machine?
Answer: B (Graph B)
Velocity ratio depends only on the design of the machine (distance moved by effort ÷ distance moved by load), so it stays the same whatever the load: a horizontal line, graph B.
A spring of length 25cm is extended to 30cm by a load of 150 N attached to one of its ends. What is the energy stored in the spring?
Answer: C (3.75 J)
Energy = ½ × force × extension = ½ × 150 × 0.05 = 3.75 J.
In the diagram above, if the atmospheric pressure is 760mm, the pressure in the chamber G is
Answer: C (830mm)
The open arm's level is 10 − 3 = 7 cm = 70 mm higher than the level on the gas side, so the gas pressure is above atmospheric: 760 + 70 = 830 mm.
A force of 15 N stretches a spring to a total length of 30cm. An additional force of 10 N stretches the spring 5cm further. Find the natural length of the spring
Answer: B (22.5cm)
10 N gives 5 cm, so 15 N gives 7.5 cm extension. Natural length = 30 − 7.5 = 22.5 cm.
Which of these statements are TRUE of pressure in liquids? I. Pressure acts equally in all directions II. Pressure decreases with depth III. Pressure at the same level of a liquid is the same IV. Pressure is dependent on the cross-sectional area of the barometer tube.
Answer: A (I and III only)
Pressure at a point acts equally in all directions and is the same at the same level. It increases (not decreases) with depth, and does not depend on the tube's area.
The mass of a specific gravity bottle is 15.2g when it is empty. It is 24.8g when filled with kerosene and 27.2g when filled with distilled water. Calculate the relative density of kerosene
Answer: D (0.80)
Mass of kerosene = 24.8 − 15.2 = 9.6 g; mass of the same volume of water = 27.2 − 15.2 = 12.0 g. R.D. = 9.6/12.0 = 0.80.
If a solid X floats in liquid P of relative density 2.0 and in liquid Q of relative density 1.5, it can be inferred that the
Answer: D (volume of P displaced is less than that of Q.)
A floating body displaces its own weight in any liquid, so the weights displaced are equal. The denser liquid P needs a smaller volume to give that weight.
The melting point of naphthalene is 78°C. What is this temperature in Kelvin?
Answer: B (351 K)
T(K) = θ(°C) + 273 = 78 + 273 = 351 K.
A motor tyre is inflated to pressure of 2.0 × 105 N m−2 when the temperature of air is 27°C. What will be the pressure in it at 87°C assuming that the volume of the tyre does not change?
Answer: B (2.4 × 105 N m−2)
At constant volume p/T is constant: p = 2.0 × 105 × 360/300 = 2.4 × 105 N m−2 (temperatures in kelvin).
A volume of water is heated from 0°C to 15°C. Which of the following diagrams correctly represents the variation of the volume with temperature?
Answer: C (Diagram C)
Water is anomalous: from 0°C to 4°C its volume decreases, then above 4°C it expands. Graph C falls to a minimum at 4°C and then rises.
Heat is supplied to a test tube containing 100g of ice at its melting point. The ice melts completely in 1 min. What is the power rating of the source of heat? (Latent heat of fusion of ice = 336 J g−1)
Answer: C (560 W)
Heat needed = 100 × 336 = 33 600 J in 60 s. Power = 33 600 ÷ 60 = 560 W.
If a room is saturated with water vapour, the temperature of the room must be
Answer: D (below or at the dew point.)
Air is saturated when its temperature has fallen to the dew point; the air cannot be saturated while it is above its dew point.
Which of the following graphs represents the variation of pressure P against volume V at constant temperature?
Answer: B (Graph B)
Boyle's law: PV = constant, so P falls as V rises along a curve (hyperbola) that never touches the axes, as in graph B.
Two similar kettles containing equal masses of boiling water are placed on a table. If the surface of one is highly polished and the surface of the other is covered with soot, which of the following observations is correct?
Answer: C (The kettle covered with soot cools down more quickly because it is a good radiator of heat)
Dull black surfaces are good radiators of heat; shiny polished surfaces are poor radiators, so the sooty kettle loses heat faster.
The equation of tranverse wave travelling along a string is given by y = 0.3 sin (0.5x − 50t) where y and x are in cm and t is in seconds. Find the maximum displacement of the particles from the equilibrium position.
Answer: D (0.3cm)
Compare with y = A sin(kx − ωt): the amplitude (maximum displacement) is A = 0.3 cm.
The sound from a source travelled to the bottom of the sea and the echo was heard 4s later. If the speed of sound in sea water is 1500 m s−1, the depth of the sea is
Answer: B (3000m)
The sound goes down and back in 4 s, so 2d = 1500 × 4 = 6000 m and d = 3000 m.
The fundamental frequency of vibration of a sonometer wire may be halved by
Answer: A (doubling the length of the wire)
f = (1/2L)√(T/m), so f ∝ 1/L: doubling the length halves the frequency. Halving the tension or doubling the mass only divides f by √2.
A pipe of length 45cm is closed at one end. Calculate the fundamental frequency of the sound wave generated in the pipe if the velocity of sound in air is 360 m s−1. (Neglect end corrections).
Answer: C (200.0 Hz)
For a closed pipe, L = λ/4, so λ = 4 × 0.45 = 1.8 m and f = 360 ÷ 1.8 = 200.0 Hz.
The note produced by a stretched string has a fundamental frequency of 400 Hz. If the length of the string is doubled while the tension in the string is increased by a factor of 4, the frequency is
Answer: B (400 Hz)
f ∝ √T/L. Multiplying T by 4 doubles f, and doubling L halves it, so f stays 400 Hz.
To produce a parallel beam of light from a concave mirror, the distance at which the lamp should be placed from the mirror is equal to
Answer: A (the focal length)
Rays from a lamp at the principal focus are reflected parallel to the principal axis (as in a torch).
Light of frequency 6.0 × 1014 Hz travelling in air is transmitted through glass or refractive index 1.5. Calculate the frequency of the light in the glass.
Answer: B (6.0 × 1014 Hz)
Frequency is set by the source and does not change on refraction; only the speed and wavelength fall by the factor 1.5. So it stays 6.0 × 1014 Hz.
An object is placed in front of a converging lens of focal length 20cm. The image is virtual and has a magnification of 2. What is the distance of the object from the lens?
Answer: B (10cm)
Virtual image with m = 2: v = −2u. Using 1/u + 1/v = 1/f: 1/u − 1/(2u) = 1/20, so 1/(2u) = 1/20 and u = 10 cm.
An object is placed directly below a glass block of thickness 3.0cm. Calculate the lateral displacement of the object if the refractive index of the glass is 1.5.
Answer: A (1.0cm)
Apparent depth = 3.0 ÷ 1.5 = 2.0 cm, so the object appears raised by 3.0 − 2.0 = 1.0 cm.
In a projection lantern of focal length f, the object distance u, is such that
Answer: D (f < u < 2f)
A projector must give a real, magnified image on a distant screen, so the slide is placed between f and 2f from the lens.
If the Nigerian flag (green, white, green) is viewed in pure yellow light, which of the following set of colours would be observed on the flag?
Answer: C (Black, yellow, black)
Green cloth reflects only green, so it absorbs yellow light and looks black. White cloth reflects whatever falls on it, so it looks yellow.
Which of the figures below illustrates the dispersion of white light through a triangular glass prism?
Answer: C (Figure C)
Each colour has a different refractive index, so white light starts to split into colours as soon as it enters the glass and spreads further on leaving, as in figure C.
Which of the following has the lowest internal resistance when new?
Answer: C (Accumulator)
A lead-acid accumulator has a very low internal resistance, which is why it can supply the large currents needed, for example, to start a car.
When a biro pen rubbed on a dry silk cloth is moved very close to a piece of paper on a dry table, the pen is found to pick up the paper. This is because
Answer: D (both the pen and the cloth are charged.)
Rubbing transfers electrons, so the pen and the cloth gain equal and opposite charges; the charged pen attracts the light paper.
In the figure above, XY is of length 1m. The value of R at balance point Z is
Answer: D (30.0Ω)
At balance R/20 = 60/40, so R = 20 × 1.5 = 30.0 Ω.
A capacitor 8μF, is charged to a potential difference of 100V. The energy stored by the capacitor is
Answer: D (4.0 × 10−2 J)
E = ½CV2 = ½ × 8 × 10−6 × 1002 = 4.0 × 10−2 J.
Two resistors, R1 = 4Ω and R2 = 5Ω, are connected in parallel across a potential difference. If P1 and P2 represent the power dissipated in R1 and R2 respectively, then the ratio P1 : P2 is
Answer: B (5 : 4)
In parallel both have the same voltage, so P = V2/R and P1 : P2 = 1/4 : 1/5 = 5 : 4.
In the circuit diagram above, calculate the current in the 12 Ω resistor if the cell has an e.m.f. of 12V and an internal resistance of 1Ω.
Answer: A (0.8A)
12 Ω and 6 Ω in parallel give 4 Ω; with the 1 Ω internal resistance the total is 5 Ω, so the cell gives 12/5 = 2.4 A. The 12 Ω branch takes 6/(12 + 6) of this: 0.8 A.
Which of the following are found in the receiver but not in the microphone of a telephone handset? I. Diaphragm II. Soft iron pole pieces III. Permanent magnet IV. Carbon blocks
Answer: C (II and III)
Both parts have a diaphragm. The earpiece (receiver) has a permanent magnet with soft-iron pole pieces and coils; the carbon granules are in the microphone.
If two parallel conductors carry currents flowing in the same direction, the conductors will
Answer: A (attract each other)
The magnetic fields of parallel currents in the same direction combine so that the wires are pulled together; opposite currents repel.
In the curve above, PQRST represents an alternating voltage of frequency 50 Hz. The time interval between points P and R on the graph is
Answer: C (1/100 s)
One cycle takes 1/50 s. From P to R is half a cycle, so the time is 1/100 s.
If light with photon energy 2eV is incident suitably on the surface of a metal with work function 3eV, then
Answer: A (no electron will be emitted)
An electron can only escape if the photon energy is at least the work function. 2 eV is less than 3 eV, so no electrons are emitted.