49 questions. Try each one, then open the answer to check yourself and read the explanation.
What is the least possible error in using a rule graduated in centimeters?
Answer: B (0.5cm)
The least possible error of a scale is half its smallest division; a rule marked in 1 cm steps gives ±0.5 cm.
Which of the following affects the period of a simple pendulum? I. Mass of the pendulum bob II. Length of the pendulum III. Acceleration due to gravity
Answer: B (II and III only)
T = 2π√(l/g), so the period depends on the length l and on g, but not on the mass of the bob.
A boy sits in a train moving with uniform speed on a straight track. If from his outstretched palm he gently tosses a coin vertically upwards, the coin will fall
Answer: D (into his palm)
The coin already shares the train's horizontal velocity, and nothing changes it while it is in the air, so it keeps pace with the boy and lands back in his palm.
A body starts from rest and moves with uniform acceleration of 6 m s−2. What distance does it cover in the third second?
Answer: A (15m)
Distance in 3 s = ½ × 6 × 3² = 27 m; in 2 s = ½ × 6 × 2² = 12 m. In the third second it covers 27 − 12 = 15 m.
A stone, Q is thrown with velocity u at an angle of 75° to the horizontal. Another stone R is thrown with the same velocity u but at an angle of 15° to the horizontal. The ranges covered by the stones will be
Answer: C (the same for Q and R)
Range = u² sin 2θ / g. sin 150° = sin 30°, so angles of 75° and 15° (which add up to 90°) give the same range.
A man weighing 800N climbs up a flight of stairs to a height of 15m in 12.5s. What is the man's average power output?
Answer: C (960W)
Work done = 800 × 15 = 12 000 J. Power = 12 000 ÷ 12.5 = 960 W.
A uniform light rod is kept in horizontal equilibrium under the influence of four forces as shown above. Which of the following equations correctly represents the condition of equilibrium for the rod?
Answer: D (F1a + F2b − F3c − F4d = 0)
Take moments about the pivot: F1 and F2 turn the rod one way, F3 and F4 the other way. Balance means F1a + F2b = F3c + F4d.
In the diagram above, the hanging mass m2 is adjusted until m1 is on the verge of sliding. The coefficient of static friction between the mass m1 and the table is
Answer: C (m2/m1)
At the point of sliding, the pull m2g equals the limiting friction μm1g, so μ = m2/m1.
A machine requires 1000 J of work to raise a load of 500N through a vertical distance of 1.5m. Calculate the efficiency of the machine.
Answer: B (75%)
Useful work output = 500 × 1.5 = 750 J. Efficiency = 750/1000 × 100% = 75%.
In an experiment to determine Young's Modulus for a wire, several loads are attached to the wire and the corresponding extensions measured. The tensile stress in each case depends on the
Answer: B (load and the radius of the wire)
Tensile stress = force ÷ cross-sectional area = load ÷ πr², so it depends on the load and the radius of the wire.
The figure above shows the heights of two liquids X and Y when some air is sucked out of the apparatus through the pump P. The diameter of the table in X is twice that of the tube in Y. What is the relative density of liquid X with respect to liquid Y?
Answer: C (3)
Both columns are held up by the same pressure difference, so ρX × 7.5 = ρY × 22.5, giving ρX/ρY = 3. The tube diameter does not matter.
If a plastic sphere floats in water (density = 1000 kg m−3) with 0.5 of its volume submerged and floats on oil with 0.4 of its volume submerged, the density of the oil is
Answer: C (1250 kg m−3)
A floating body displaces its own weight in both liquids: 0.5V × 1000 = 0.4V × ρ, so ρ = 500/0.4 = 1250 kg m−3.
A platinum resistance thermometer wire has a resistance of 5 ohms at 0°C and 5.5 ohms at 100°C. Calculate the temperature of the wire when the resistance is 5.2 ohms.
Answer: C (40°C)
θ = (5.2 − 5.0)/(5.5 − 5.0) × 100 = 0.2/0.5 × 100 = 40°C.
A bridge made of steel is 600m long. What is the daily variation in its length if the night-time and day-time temperatures are 10°C and 35°C respectively. The linear expansivity of steel is 0.000012 C−1
Answer: C (18.00cm)
Change in length = 600 × 0.000012 × (35 − 10) = 0.18 m, which is 18.00 cm.
One of the most important applications of bi-metallic strip is found in the construction of
Answer: A (a thermostat)
A bimetallic strip bends when heated because its two metals expand differently; a thermostat uses this bending to switch a circuit on and off.
At constant pressure, the density of a fixed mass of gas is
Answer: C (inversely proportional to its temperature)
At constant pressure V ∝ T (Charles's law). Density = mass/volume, so density ∝ 1/T.
How much heat is absorbed when a block of copper of mass 0.05kg and specific heat capacity 390 J kg−1 K−1 is heated from 20°C to 70°C?
Answer: B (9.75 × 102 J)
Q = mcθ = 0.05 × 390 × 50 = 975 J = 9.75 × 102 J.
A block of ice floats on water inside a container. If the block of ice gets completely melted, the level of water in the container will
Answer: B (remain the same)
Floating ice displaces its own weight of water. When it melts it becomes exactly that much water, which fills the space it displaced, so the level does not change.
The space between the double glass walls of a thermos flask is evacuated and the two surfaces facing the evacuated space are silvered. The residual source of heat loss takes place by
Answer: C (conduction through the stopper and the glass)
The vacuum stops conduction and convection across the walls and the silvering cuts radiation, so the heat that still escapes leaks by conduction through the stopper and along the glass.
The equation of a wave is y = 0.005 sin [π(0.5x − 200t)] where x and y are in metres and t is in seconds. What is the velocity of the wave?
Answer: B (400 m s−1)
For y = A sin(kx − ωt) the wave speed is v = ω/k. Here v = 200/0.5 = 400 m s−1 (a common factor π cancels).
Which of the following characteristics of a wave is used in the measurement of the depth of the sea?
Answer: D (Reflection)
Echo sounding sends a sound pulse down and times its echo, which is the pulse reflected from the sea bed.
A note is the octave of another note if it has
Answer: A (a frequency twice that of the first note)
A note one octave above another has exactly twice its frequency.
What is the frequency of the sound made by a siren having a disc with 32 holes and making 25 revolutions per second?
Answer: C (800 Hz)
Each hole gives one puff of air per revolution: f = 32 × 25 = 800 Hz.
Which of the following properties make the convex mirror useful as a driving mirror? I. The image is real II. The image is erect III. It has a wide field of view IV. The image is magnified.
Answer: C (II and III)
A convex mirror always gives an upright (erect), diminished, virtual image and covers a wide field of view, which is what a driver needs.
When an object is placed very close to the pole of a concave mirror, the virtual image obtained is
Answer: D (enlarged and upright)
An object inside the focal length of a concave mirror gives a virtual image that is upright and magnified (as in a shaving mirror).
A concave mirror has a radius of curvature of 36cm. At what distance from the mirror should an object be placed to give a real image three times the size of the object?
Answer: B (24cm)
f = 36/2 = 18 cm and v = 3u. 1/u + 1/(3u) = 1/18 gives 4/(3u) = 1/18, so u = 24 cm.
Which of the following statements is CORRECT about a long-sighted boy who does not put on glasses?
Answer: D (Parallel rays of light are focused behind his retina.)
A long-sighted eye is too short (or its lens too weak), so with the eye relaxed even parallel rays would meet behind the retina; near objects are the ones he cannot see clearly.
The speed of light in air is 3 × 108 m s−1. What is the speed in glass with a refractive index of 1.50?
Answer: C (2.0 × 108 m s−1)
n = speed in air ÷ speed in glass, so v = 3 × 108 ÷ 1.5 = 2.0 × 108 m s−1.
If the refractive index of a medium in air is 2.0, what is the critical angle for this medium?
Answer: A (30°)
sin c = 1/n = 1/2, so c = 30°.
Which of the following arrangements of the components of electromagnetic spectrum is in ascending order of wavelengths?
Answer: B (Gamma rays, x-rays, ultraviolet rays, infra-red rays)
From shortest to longest wavelength: gamma rays, X-rays, ultraviolet, visible light, infra-red, radio waves.
The diagram above represents the field pattern obtained by bringing the poles of two magnets near each other. The poles must be
Answer: B (S-S poles)
The lines push away from each other and leave a neutral point between the poles, so the poles are alike; the arrows point into both poles, and field lines enter at south poles.
The angle between the direction of the earth's magnetic field and the horizontal is called the
Answer: D (angle of dip.)
The angle the earth's field makes with the horizontal is the angle of dip (inclination); declination is the angle between magnetic and geographic north.
Calculate the force acting on an electron of charge 1.6 × 10−19 C placed in an electric field of intensity 108 V m−1
Answer: A (1.6 × 10−11 N)
F = qE = 1.6 × 10−19 × 108 = 1.6 × 10−11 N.
When an ebonite rod is rubbed with fur, it has
Answer: B (a negative charge)
Rubbing moves electrons from the fur to the ebonite, so the ebonite becomes negatively charged.
Which of the following factors has no effect on the e.m.f. of a primary cell?
Answer: B (size of the cell)
The e.m.f. of a cell is set by the chemicals (plates and electrolyte) used; a bigger cell of the same type has the same e.m.f., only more capacity.
A wire of length 15m made of a material of resistivity 1.8 × 10−6 Ω m has a resistance of 0.27Ω. Determine the area of the wire
Answer: B (1.0 × 10−4 m2)
R = ρL/A, so A = ρL/R = 1.8 × 10−6 × 15 ÷ 0.27 = 1.0 × 10−4 m2.
The diagram above shows a meter bridge in which two of the arms contain resistances R and 2Ω. A balance point is obtained at 60cm from the left end. Calculate the value of R.
Answer: C (3.0Ω)
At balance R/2 = 60/40, so R = 2 × 1.5 = 3.0 Ω.
The circuit diagram above contains four ammeters W, X, Y and Z. Which of the following statements about the ammeter reading is correct?
Answer: C (The readings of W and Y are equal and each is greater than that of X)
W, Z and Y are all in the main line, so they carry the full current. X is in only one of the two parallel branches, so it carries less.
A 5-V battery is connected across the plates of a 2.0μF uncharged parallel plate capacitor. The charge on the capacitor after a long time is
Answer: B (10.0μC)
Q = CV = 2.0 μF × 5 V = 10.0 μC.
Which of the following apparatus will require the smallest fuse rating for its protection?
Answer: A (60W, 240V)
Current I = P/V: 60/240 = 0.25 A, 60/40 = 1.5 A, 40/12 ≈ 3.3 A, 40/5 = 8 A. The smallest current needs the smallest fuse.
A capacitor of 10μF is connected across a cell of 12 volts as shown above. Calculate the energy stored in the capacitor.
Answer: A (7.2 × 10−4 J)
E = ½CV2 = ½ × 10 × 10−6 × 122 = 7.2 × 10−4 J.
The heat produced in a conductor carrying an electric current is
Answer: D (directly proportional to the square of the current, the resistance and the time.)
Joule's law: heat H = I2Rt.
The maximum permissible current through a galvanometer G of internal resistance 10Ω is 0.05A. A resistance R is used to convert G into a voltmeter with a maximum reading of 100V. Find the value of R and how it is connected to G.
Answer: C (1990 ohms in series)
A voltmeter needs a large resistance in series. Total resistance = 100/0.05 = 2000 Ω, so R = 2000 − 10 = 1990 Ω in series.
In alternating current theory, the units of impedance, r.m.s. voltage and resonance frequency are respectively equal to
Answer: B (ohm, volt and hertz)
Impedance is a kind of resistance (ohm), r.m.s. voltage is a voltage (volt) and frequency is in hertz.
In A.C. circuit theory, the root mean square (r.m.s) current, Irms, and the peak (maximum) current Io are related by
Answer: B (Irms = Io/√2)
For a sinusoidal current the r.m.s. value is the peak value divided by √2 (about 0.707 Io).
Which of the following graphs correctly illustrates the number of remaining atoms during a radioactive decay?
Answer: B (Graph B)
The number of undecayed atoms starts at its largest value and falls exponentially, halving every half-life and approaching zero; graph B shows this curve starting from the initial number.
The threshold frequency for photoelectric effect depends on the
Answer: C (material of the photocathode)
Threshold frequency f0 = work function ÷ h, and the work function is a property of the metal (the photocathode material).
After three half lifes, the fraction of a radioactive material that has decayed is
Answer: D (7/8)
After three half-lives ½ × ½ × ½ = 1/8 remains, so 1 − 1/8 = 7/8 has decayed.
2713Al + 10n → 2411Na + X
In the nuclear reaction above, the product denoted by X is
Answer: D (an alpha particle.)
Mass numbers: 27 + 1 = 24 + 4; atomic numbers: 13 + 0 = 11 + 2. X has A = 4 and Z = 2, which is an alpha particle (42He).