48 questions. Try each one, then open the answer to check yourself and read the explanation.
Which of the following diagrams correctly represents the relationship between the time (T) of swing of a simple pendulum and its length (l)?
Answer: C (C)
T = 2π√(l/g), so T² is proportional to l and the graph of T² against l is a straight line through the origin, as in C.
Which of the following are the correct SI units of the quantities indicated? I. N (Force) II. N m−1 (Torque) III. Watt (Power) IV. kg m s−2 (Momentum)
Answer: D (I and III only.)
Force is in newtons and power in watts. Torque is in N m (not N m−1) and momentum in kg m s−1 (not kg m s−2).
A lorry travels 10 km northwards, 4 km eastwards, 6 km southwards and 4 km westwards to arrive at a point T. What is the total displacement?
Answer: B (4 km north)
East and west cancel (4 − 4 = 0). North–south: 10 − 6 = 4 km north.
Two forces whose resultant is 100 N, are at right angles to each other. If one of them makes an angle of 30° with the resultant, determine its magnitude.
Answer: D (86.6 N)
The component of the resultant along that force is 100 cos 30° = 86.6 N.
Which of the following quantities are scalars? I. Electrical potential II. Torque III. Momentum IV. Kinetic energy
Answer: D (I and IV only.)
Electrical potential and kinetic energy have size only. Torque and momentum have direction, so they are vectors.
A particle starts from rest and moves with a constant acceleration of 0.5 m s−2. The distance covered by the particle in 10 s is
Answer: C (25.0 m)
s = ½at² = ½ × 0.5 × 100 = 25 m.
When taking a penalty kick, a footballer applies a force of 30.0 N for a period of 0.05 s. If the mass of the ball is 0.075 kg, calculate the speed with which the ball moves off.
Answer: C (20.00 m s−1)
Impulse = change in momentum: 30 × 0.05 = 0.075 × v, so v = 1.5/0.075 = 20 m s−1.
A 20-toothed gear wheel drives a 60-toothed one. If the angular speed of the smaller wheel is 120 rev s−1, the angular speed of the larger wheel is
Answer: B (40 rev s−1)
The same number of teeth pass the contact point on each wheel, so speed × teeth is equal: 120 × 20 = ω × 60, giving ω = 40 rev s−1. The bigger wheel turns more slowly.
The figure above shows the displacement – time graphs for three different motions. Which of the following statements is correct?
Answer: B (Graph 1 corresponds to zero velocity)
Velocity is the slope of a displacement–time graph. Graph 1 is horizontal, so its velocity is zero; graph 2 slopes down (negative direction) and graph 3 is steepest and positive.
The figures above show three different ways of hanging a heavy picture from a hook. The tension in the string would be
Answer: B (greatest in Y)
Each string's vertical pulls must add up to the weight. The flatter the strings, the smaller their vertical share, so the tension must be larger. The strings in Y are the flattest.
How long will it take a 60 kg man to climb a height of 22 m if he expended energy at the rate of 0.25 kW? [g = 10 m s−2]
Answer: D (52.8 s.)
Work = mgh = 60 × 10 × 22 = 13 200 J. Time = 13 200 ÷ 250 = 52.8 s.
A force, 10 N, drags a mass 10 kg on a horizontal table with an acceleration of 0.2 m s−2. If the acceleration due to gravity is 10 m s−2, the coefficient of friction between the moving mass and the table is
Answer: B (0.08)
Net force = 10 × 0.2 = 2 N, so friction = 10 − 2 = 8 N. μ = 8/(10 × 10) = 0.08.
Which of the following graphs correctly describes the variation of the mechanical advantage with load for a simple machine whose velocity ratio is 3?
Answer: B (B)
As the load grows, friction and the weight of moving parts matter less, so the MA rises quickly at first and then levels off below the velocity ratio, as in B.
A body whose mass is 2 kg and has a volume of 500 cm3 just floats when completely immersed in a liquid. Calculate the density of the liquid.
Answer: B (4.0 × 103 kg m−3)
It just floats when fully immersed, so the liquid's density equals the body's: 2 ÷ (500 × 10−6) = 4.0 × 103 kg m−3.
When one arm of a U-tube manometer is connected to a gas supply, the levels of mercury in the two arms of the U-tube are as shown in the diagram above. If the atmospheric pressure is 76.0 cm Hg, the gas pressure is
Answer: D (85.9 cm Hg)
The mercury in the open arm stands 13.4 − 3.5 = 9.9 cm higher, so the gas pressure is 76.0 + 9.9 = 85.9 cm Hg.
The product PV where P is pressure and V is volume has the same unit as
Answer: C (energy)
PV has units N m−2 × m3 = N m = J, the unit of energy.
The amount of heat needed to raise the temperature of 10 kg of copper by 1 K is its
Answer: B (heat capacity)
The heat needed to raise a whole body by one degree is its heat capacity; specific heat capacity refers to 1 kg.
A tap supplies water at 25°C while another supplies water at 75°C. If a man wishes to bathe with water at 40°C, the ratio of the mass of cold water to the mass of hot water required is
Answer: C (7 : 3)
Heat lost by hot = heat gained by cold: mh × 35 = mc × 15, so mc : mh = 35 : 15 = 7 : 3.
Which of the following graphs clearly illustrates the temperature change which takes place as a piece of ice at − 10°C is heated slowly?
Answer: A (A)
The temperature rises from −10°C to 0°C, stays at 0°C while the ice melts, rises to 100°C and stays there while the water boils, as in A.
When heat is applied to one end of a metal rod, the molecules at the other end soon begin to vibrate with greater amplitude than before because heat has been transferred by
Answer: C (conduction)
In a solid, heat passes from molecule to molecule by their vibrations (and by free electrons in metals): conduction.
Which of the following media allow the transmission of sound waves through them? I. Air II. Liquids III. Solids
Answer: D (I, II and III.)
Sound travels through any material medium: gases, liquids and solids.
The diagram above shows two waveforms X and Y. If the frequency of X is 30 Hz, what is the frequency of Y?
Answer: D (75 Hz)
In the same time Y completes 2½ waves while X completes one, so fY = 2.5 × 30 = 75 Hz.
Which of the following properties is/are common to all waves? I. Diffraction II. Refraction III. Interference
Answer: D (I, II and III.)
All waves, transverse or longitudinal, can be diffracted, refracted and made to interfere.
A piano wire 0.5 m long has a total mass of 0.01 kg and is stretched with a tension of 800 N. Calculate the frequency of the wire when it sounds its fundamental note.
Answer: A (200 Hz)
Mass per unit length μ = 0.01/0.5 = 0.02 kg m−1. f = (1/2L)√(T/μ) = (1/1) × √(800/0.02) = 200 Hz.
A note is called an octave of another note when
Answer: A (its frequency is twice that of the first note)
A note one octave above another has double its frequency.
Which of the following factors affects the speed of sound in air? I. Temperature II. Pressure III. Frequency
Answer: A (I only)
The speed of sound in air rises with temperature; at constant temperature it does not depend on pressure or frequency.
The speed of sound in air at sea-level is 340 m s−1 while that of light is 300 000 km s−1. How far (to the nearest metre) from the centre of a thunderstorm is an observer who hears a thunder 2 s after a lightening flash?
Answer: D (680 m)
Light arrives almost instantly, so the 2 s delay is the sound's travel time: 340 × 2 = 680 m.
A slight loading of a tuning fork has the effect of
Answer: C (decreasing its frequency)
Adding mass to the prongs makes them vibrate more slowly, so the frequency falls.
Two strings of the same length and under the same tension give notes of frequencies in the ratio 4 : 1. The masses of the strings are in the corresponding ratio of
Answer: D (1 : 16.)
f ∝ 1/√m at fixed length and tension, so m ∝ 1/f². A frequency ratio 4 : 1 gives a mass ratio 1 : 16.
To obtain a magnification of 2.5, how far should an object be placed from the pole of a thin converging lens of focal length 0.20 m?
Answer: C (0.28 m)
For a real image v = 2.5u. 1/u + 1/(2.5u) = 1/0.2 gives 3.5/(2.5u) = 5, so u = 0.28 m.
In the figure above, what is the angle of reflection of the ray of light at mirror M2?
Answer: B (60°)
The ray strikes M1 at 30° to its normal and leaves at 30° below the horizontal. M2 is horizontal, so the ray meets it at 60° to its (vertical) normal and reflects at 60°.
An object is placed 10 cm in front of a concave mirror of focal length 15 cm. What is the position and nature of the image formed?
Answer: A (30 cm and virtual)
The object is inside the focal length, so the image is virtual. 1/v = 1/15 − 1/10 = −1/30, so it is 30 cm behind the mirror.
Which of the following phenomena explain the formation of a mirage? I. Reflection II. Refraction III. Diffraction
Answer: A (I and II only)
Light from the sky is refracted through layers of air of different temperature and finally totally reflected near the hot ground, so refraction and (total internal) reflection cause a mirage.
When white light is dispersed by a spectrometer, the component having the shortest wavelength is
Answer: C (violet)
Violet has the shortest wavelength of visible light and red the longest.
Which of the following statements is TRUE of ultra-violet, visible and infra-red rays?
Answer: B (Ultra-violet rays have shorter wavelengths than infra-red rays and produce fluorescence)
Ultraviolet has a shorter wavelength than visible light and infra-red, and it makes some substances fluoresce.
E, F and G are yellow, red and cyan transparent light filters respectively. The colour of a white opaque object when viewed through the arrangement of the filters above is
Answer: C (black)
The yellow filter passes red and green, the red filter then passes only red, and the cyan filter (green + blue) absorbs red. No light gets through, so the object looks black.
The wire X in the figure above is at right angles to the plane of the paper and carries a current into the paper. At which of the points labelled 1 - 4 will the magnetic flux density due to this current be in the same direction as that of the horizontal component of the earth's magnetic field?
Answer: C (3)
A current into the paper makes clockwise field lines. Going clockwise, the field at point 3 (to the left of the wire) points up the page, towards magnetic north, like the earth's horizontal field.
A spectrum of sunlight is said to be impure when
Answer: C (the different colours in it overlap)
In an impure spectrum the colours overlap instead of being separated cleanly.
A cell of internal resistance 2 ohms supplies current to a 6-ohm resistor. The efficiency of the cell is
Answer: D (75.0%)
Efficiency = useful power ÷ total power = R/(R + r) = 6/8 = 75%.
In the circuit diagram above, the ammeter reads a current of 3 amps, when R is 5 ohms and reads 6 amps when R is 2 ohms. The value of the unknown resistance X is
Answer: A (1)
E = 3(5 + X) = 6(2 + X). So 15 + 3X = 12 + 6X, giving X = 1 Ω.
Which of the following combinations of 2 μF capacitors will give an effective capacitance of 3 μF across terminal XY?
Answer: A (A)
In A, two 2 μF in series give 1 μF, and the third 2 μF in parallel with them adds to 3 μF.
A household refrigerator is rated 200 watts. If electricity costs 5k per kWh, what is the cost of operating it for 20 days?
Answer: A (N4.80)
Energy = 0.2 kW × 24 h × 20 = 96 kWh. Cost = 96 × 5k = 480k = N4.80.
Which of the following instruments consumes the highest current? (A. Electric iron: 250 V, 1 kW; B. Television set: 220 V, 110 W; C. Torchlight: 6 V, 30 W; D. Immersion heater: 110 V, 500 W)
Answer: C (Torchlight)
I = P/V: iron 4 A, television 0.5 A, torch 5 A, heater 4.55 A. The torchlight draws the most.
Which of the following ammeters may be used to measure alternating currents? I. Moving-coil ammeter II. Moving-iron ammeter III. Hot-wire ammeter
Answer: B (II and III only)
Moving-iron and hot-wire meters respond the same way whichever way the current flows. A moving-coil meter's pointer reverses with the current, so it only measures d.c.
The principle of operation of an induction coil is based on
Answer: C (Faraday's law)
An induction coil makes a high e.m.f. by electromagnetic induction, described by Faraday's law.
A dynamo primarily converts
Answer: A (mechanical energy into electrical energy)
A dynamo (generator) turns the mechanical energy of rotation into electrical energy.
In a certain fusion reaction, a deuteron (21H) interacts with a triton (31H) and produces an α-particle (42He) and a second product. The second product is
Answer: C (a neutron)
Mass numbers: 2 + 3 = 4 + 1, and charges: 1 + 1 = 2 + 0. The missing particle has mass number 1 and charge 0: a neutron.
A particle is injected perpendicularly into an electric field. It travels along a curved path as depicted in the figure above. The particle is
Answer: B (an electron)
The field points up the page but the particle bends downwards, against the field, so it is negatively charged: an electron.