48 questions. Try each one, then open the answer to check yourself and read the explanation.
Which of the following quantities has the same unit as the watt?
Answer: D (Force × velocity)
Power = work/time = force × distance/time = force × velocity, so N m s−1 is the same as the watt.
The external and internal diameters of a tube are measured as (32 ± 2)mm and (21 ± 1)mm respectively. Determine the percentage error in the thickness of the tube.
Answer: A (27%)
Thickness = (32 − 21)/2 = 5.5 mm. The errors add: (2 + 1)/2 = 1.5 mm. Percentage error = 1.5/5.5 × 100 ≈ 27%.
The diagram above shows a velocity-time graph representing the motion of a car. Find the total distance covered during the acceleration and retardation periods of the motion.
Answer: A (75m)
Distance = area under the graph. Acceleration (0–10 s): ½ × 10 × 10 = 50 m. Retardation (40–45 s): ½ × 5 × 10 = 25 m. Total = 75 m.
Two forces of magnitudes 7N and 3N act at right angles to each other. The angle θ between the resultant and the 7N force is given by
Answer: C (tan θ = 3/7)
Draw the 7 N and 3 N forces as two sides of a right-angled triangle; the resultant is the hypotenuse, and tan θ = opposite/adjacent = 3/7.
An aeroplane lands on a runway at a speed of 180 km h−1 and is brought to a stop uniformly in 30 seconds. What distance does it cover on the runway before coming to rest?
Answer: C (750m)
180 km h−1 = 50 m s−1. With uniform slowing, average speed = 25 m s−1, so distance = 25 × 30 = 750 m.
A rocket burns fuel at the rate of 10 kg s−1 and ejects it with a velocity of 5 × 103 m s−1. The thrust exerted by the gas on the rocket is
Answer: B (5.0 × 104 N)
Thrust = rate of change of momentum = (mass per second) × velocity = 10 × 5 × 103 = 5.0 × 104 N.
The force experienced by an object of mass 60.0kg in the moon's gravitational field is 1.002 × 102 N. What is the intensity of the gravitational field?
Answer: B (1.67 N kg−1)
Field intensity = force per unit mass = 100.2 ÷ 60.0 = 1.67 N kg−1.
Which of the following correctly describes the energy changes in the generation of light by a hydroelectric power station?
Answer: B (Potential → mechanical → electrical → light)
Water stored behind the dam has potential energy; falling, it turns the turbines (mechanical), the generators produce electrical energy, and lamps turn it into light.
A plane inclined at angle θ has a velocity ratio of 10 : 1. The inclination of the plane to the horizontal is given by
Answer: D (sin θ = 1/10)
For an inclined plane, V.R. = length of slope ÷ height = 1/sin θ. So 1/sin θ = 10 and sin θ = 1/10.
A weightless vessel of dimensions 4m × 3m × 2m is filled with a liquid of density 1000 kg m−3 and sealed. What is the maximum pressure this container can exert on a flat surface? [g = 10 m s−2]
Answer: B (4 × 104 N m−2)
Pressure is greatest when the vessel stands on its smallest face (3 m × 2 m), so the liquid is 4 m deep: p = hρg = 4 × 1000 × 10 = 4 × 104 N m−2.
In the figure above the weight X is held in position by pulling the rope KLM in the direction LM. Which of the following diagrams shows the force acting at point L?
Answer: B (Diagram B)
Three forces act at L: the weight (down), the pull along LM (horizontal) and the tension along LK (up and to the left). Drawn head to tail they close a triangle with a vertical side, a horizontal side and a slanting side, as in diagram B.
In the diagram above, a lever of length 200m is used to lift a load of mass 180kg. The pivot at P is 20m from the load. What minimum force, F, must be applied at the end of the lever? [g = 10 m s−2]
Answer: D (200 N)
Take moments about P: 180 × 10 × 20 = F × 180 (the effort is 200 − 20 = 180 m from P), so F = 200 N.
An object of mass 400g and density 600 kg m−3 is suspended with a string so that half of it is immersed in paraffin of density 900 kg m−3. The tension in the string is
Answer: A (1.0 N)
Volume = 0.4/600 m3; half of it displaces 900 × 0.4/1200 = 0.3 kg of paraffin, so upthrust = 3 N. Weight = 4 N, so tension = 4 − 3 = 1.0 N (g = 10 m s−2).
The thermometric property of the thermocouple is that its
Answer: A (e.m.f. changes with temperature)
A thermocouple produces an e.m.f. that depends on the temperature difference between its two junctions.
A metal rod 800mm long is heated from 10°C to 95°C. If it expands by 1.36mm, the linear expansivity of the metal is
Answer: D (2.0 × 10−5 K−1)
α = extension ÷ (original length × temperature rise) = 1.36 ÷ (800 × 85) = 2.0 × 10−5 K−1.
When the volume of a given mass of gas is halved and its temperature doubled, the pressure
Answer: B (increases by a factor of 4)
pV/T is constant, so p ∝ T/V. Doubling T and halving V multiplies p by 2 × 2 = 4.
200g of water at 90°C is mixed with 100g of water at 30°C. What is the final temperature?
Answer: C (70°C)
Heat lost = heat gained: 200(90 − θ) = 100(θ − 30), so 18 000 − 200θ = 100θ − 3000 and θ = 70°C.
A block of ice at 0°C is put in an open vessel and heated uniformly until half the water boils off. Which of the following graphs best illustrates the change in temperature during the process?
Answer: D (Graph D)
The temperature stays at 0°C while the ice melts, rises steadily as the water warms, then stays at 100°C while the water boils; graph D shows flat, rising, flat.
The melting point of a solid is given as 80°C. If 105 J of heat energy is required at this temperature to melt 10g of the solid, the specific latent heat of fusion of the solid is
Answer: C (1.00 × 107 J kg−1)
L = Q/m = 105 ÷ 0.010 = 1.00 × 107 J kg−1.
The figure shows a stationary wave in a closed tube. The relationship between L and the wavelength λ of the stationary wave is
Answer: D (4L = 3λ.)
From the open end (antinode) to the closed end (node) the tube holds three quarter-wavelengths: L = 3λ/4, so 4L = 3λ.
Which of the following waves can propagate through a vacuum?
Answer: D (Infra-red waves.)
Sound waves of any kind need a material medium; infra-red is an electromagnetic wave and travels through a vacuum.
Radio waves emitted from an antenna are picked up by a radar after reflection from an aircraft in 4 × 10−3 s. How far is the aircraft from the antenna? [c = 3 × 108 m s−1]
Answer: A (6.0 × 102 km)
The waves go there and back, so distance = c × t/2 = 3 × 108 × 2 × 10−3 = 6.0 × 105 m = 6.0 × 102 km.
The fundamental frequency of vibration (f) of a wire is measured as a function of the tension (T) in the wire. Which of the following curves adequately represents the data?
Answer: C (Graph C)
f ∝ √T, so f2 ∝ T: a graph of f2 against T is a straight line through the origin, as in graph C.
Two mirrors, M1, M2 are inclined at right angles as shown above. Calculate the angle of reflection of the ray of light at mirror M2.
Answer: C (60°)
At M1 the ray meets the normal at 30° and leaves 30° below the horizontal. It then strikes the horizontal mirror M2 at 30° to its surface, i.e. 60° to its normal, so the angle of reflection is 60°.
Which of the following expressions gives the linear magnification produced by a concave mirror of radius of curvature r, if u and v are the object and image distances respectively?
Answer: B (2v/r − 1)
m = v/u and 1/u = 1/f − 1/v, so m = v/f − 1. With f = r/2 this gives m = 2v/r − 1.
If the focal length of a camera lens is 20cm, the distance from the film at which the lens must be set to produce a sharp image of an object 100cm away is
Answer: C (25cm)
1/v = 1/f − 1/u = 1/20 − 1/100 = 4/100, so v = 25 cm.
Which of the following may be used to explain a mirage? I. Layers of air near the road surface have varying refractive indices in hot weather II. Road surfaces sometimes become good reflectors in hot weather. III. Light from the sky can be reflected upwards after coming close to the road surface.
Answer: C (I and III only)
Hot air near the road has a lower refractive index, so light from the sky bends and is totally internally reflected upwards, looking like water. The road itself does not become a mirror.
A beam of light is incident from air to water at an angle of 30°. Find the angle of refraction if the refractive index of water is 4/3.
Answer: C (22°)
sin r = sin 30° ÷ (4/3) = 0.5 × 0.75 = 0.375, so r ≈ 22°.
The property of the eye known as its power of accommodation is controlled by the
Answer: D (ciliary muscles.)
The ciliary muscles change the thickness of the eye lens, which changes its focal length so it can focus near and far objects.
Which of the following correctly explain(s) why a green leaf appears green in bright daylight? I. It absorbs only the green component of sunlight. II. It absorbs all colours in sunlight except green III. It reflects only the green component of sunlight.
Answer: D (II and III only)
A green leaf absorbs the other colours of white light and reflects only green, which is what reaches our eyes.
The field that results from the contact of a positively charged ball with the inner wall of an uncharged hollow conducting sphere is
Answer: D (outside the sphere.)
When the ball touches the inside wall, all its charge flows to the outer surface of the hollow conductor. There is then no field inside, only outside.
A horizontal component of the earth's magnetic field and the magnetic field of a straight wire X carries current into the plane of a paper. Which of the following figures correctly illustrates the resultant magnetic field pattern in the horizontal plane?
Answer: A (Figure A)
The circular field of the wire adds to the earth's straight field on one side and cancels it on the other, giving distorted loops near the wire and a neutral point on one side, as in figure A.
Which of the following correctly explain(s) why soft iron is preferred to steel in electromagnets? I. Soft iron is more readily magnetized than steel II. Soft iron is more readily demagnetized than steel III. Soft iron retains magnetism more than steel.
Answer: C (I and II only)
Soft iron magnetises strongly when the current flows and loses its magnetism when it stops, so the electromagnet can be switched on and off. Steel keeps its magnetism.
A current-carrying conductor experiences a force when placed in a magnetic field because the
Answer: B (magnetic field of the current interacts with external magnetic field)
The current produces its own magnetic field around the conductor, and this field combines with the external field, giving a force (the motor effect).
A simple cell with mercury-amalgamated zinc electrode prevents
Answer: A (local action)
Impurities in ordinary zinc form tiny cells that eat away the zinc (local action); coating the zinc with mercury stops this.
The terminal voltage of a battery is 4.0 V when supplying a current of 2.0A, and 2.0V when supplying a current of 3.0A. The internal resistance of the battery is
Answer: C (2.0Ω)
E = V + Ir: E = 4 + 2r and E = 2 + 3r. Subtracting gives r = 2.0 Ω.
The current I in the figure above is
Answer: A (4.00A)
Each branch has two 2 Ω resistors in series (4 Ω); the two branches in parallel give 2 Ω. Adding the 1 Ω gives 3 Ω, so I = 12/3 = 4.00 A.
A current of 100 mA passes through a conductor for 2 minutes. The quantity of electricity transported is
Answer: C (12C)
Q = It = 0.100 A × 120 s = 12 C.
A parallel plate capacitor of area 10 cm2 in vacuum has a capacitance of 10−2 μF. What is the distance between the plates? (εo = 9 × 10−12 F m−1)
Answer: B (9 × 10−7 m)
d = εoA/C = 9 × 10−12 × 10 × 10−4 ÷ 10−8 = 9 × 10−7 m.
In the network shown above, determine the potential difference across the 5μF capacitor.
Answer: D (18 V)
The 5 μF and 15 μF are in series across 24 V (the 20 μF is in parallel and does not affect them). Series C = 5 × 15/20 = 3.75 μF, Q = 3.75 × 24 = 90 μC, so V = 90/5 = 18 V.
A 40-W instrument has a resistance of 90Ω. On what voltage should it be operated normally?
Answer: A (60 V)
P = V2/R, so V = √(PR) = √(40 × 90) = √3600 = 60 V.
Which of the following devices may be used to step up the voltage in a d.c. circuit?
Answer: D (An induction coil.)
A transformer needs a.c. An induction coil uses a make-and-break switch to interrupt the d.c., producing a high induced voltage.
The primary aim in high tension transmission is to
Answer: A (minimize electrical energy losses due to heat production)
At high voltage the same power is sent with a small current, so the I2R heat lost in the cables is small.
Determine the inductive reactance when a 30.0 mH inductor with a negligible resistance is connected to a 1.30 × 103 Hz oscillator.
Answer: C (245.0Ω)
XL = 2πfL = 2 × 3.142 × 1300 × 0.030 ≈ 245.0 Ω.
Which of the following statements correctly describe(s) cathode rays? I. They consist of tiny particles carrying negative electric charges II. They are deflected in a magnetic field but not in an electric field. III. They consist of fast moving neutrons and deflected in an electric field.
Answer: A (I only)
Cathode rays are streams of fast electrons (negative particles); they are deflected by both electric and magnetic fields, and they are not neutrons.
Natural radioactivity is the random spontaneous disintegration of the nuclei of heavy isotopes of certain elements with the emission of
Answer: B (α, β and γ-rays)
Radioactive nuclei give out alpha particles, beta particles and gamma rays. X-rays come from electrons, not nuclei.
Which of the following are produced after a nuclear fusion process? I. One heavy nucleus II. Neutrons III. Protons IV. Energy
Answer: B (I and IV)
In fusion, light nuclei join to form one heavier nucleus, and the lost mass is released as energy.
The kinetic energy of a photoelectron liberated from a metallic surface depends on the
Answer: D (frequency of the incident radiation.)
Einstein's equation: ½mv2max = hf − W, so the kinetic energy depends on the frequency; intensity only changes the number of electrons.