45 questions. Try each one, then open the answer to check yourself and read the explanation.
Which of the following is the most suitable for use as an altimeter?
Answer: D (An aneroid barometer)
An aneroid barometer is small, light and has no liquid, so it can be carried in an aircraft and its scale marked in heights.
A body of weight W N rests on a smooth plane inclined at an angle θ° to the horizontal. What is the resolved part of the weight in Newtons along the plane?
Answer: A (W sin θ)
The component of the weight along a slope of angle θ is W sin θ; the component at right angles to it is W cos θ.
A small metal ball is thrown vertically upwards from the top of a tower with an initial velocity of 20 m s−1. If the ball took a total of 6 s to reach ground level, determine the height of the tower [g = 10 m s−2]
Answer: A (60 m)
Taking up as positive, displacement after 6 s = ut − ½gt² = 20 × 6 − 5 × 36 = −60 m. The ball ends 60 m below its start, so the tower is 60 m high.
An object moves with uniform speed round a circle. Its acceleration has
Answer: B (constant magnitude and varying direction)
The centripetal acceleration v²/r has a fixed size but always points to the centre, so its direction keeps changing.
A body of mass 100 g moving with a velocity of 10.0 m s−1 collides with a wall. If after the collision, it moves with a velocity of 2.0 m s−1 in the opposite direction, calculate the change in momentum.
Answer: B (1.2 N s)
Initial momentum = 0.1 × 10 = 1.0 N s; final = 0.1 × (−2) = −0.2 N s. Change = −0.2 − 1.0 = −1.2 N s, a size of 1.2 N s.
Find the tension T1 in the diagram above if the system is in equilibrium. [g = 10 m s−2]
Answer: B (100/√3 N)
The 100 N weight is held by the vertical part of T2: T2 cos 30° = 100, so T2 = 200/√3 N. The horizontal parts balance: T1 = T2 sin 30° = 100/√3 N.
A wheel and axle have radii 80 cm and 10 cm respectively. If the efficiency of the machine is 0.85, an applied force of 1200 N to the wheel will raise a load of
Answer: C (8160.0 N)
VR = 80/10 = 8. MA = 0.85 × 8 = 6.8. Load = 6.8 × 1200 = 8160 N.
A body is under the action of a force F such that the force – displacement graph of the body is semicircular as shown above. The work done on the body by the force in moving through 24 metres is
Answer: B (72π J)
Work = area under the graph = area of a semicircle of radius 12 = ½π × 12² = 72π J.
A 20 kg mass is to be pulled up a slope inclined at 30° to the horizontal. If the efficiency of the plane is 75%, the force required to pull the load up the plane is [g = 10 m s−2].
Answer: C (133.3 N)
VR = 1/sin 30° = 2, so MA = 0.75 × 2 = 1.5. Effort = 200 ÷ 1.5 ≈ 133.3 N.
The spiral spring of a spring balance is 25.0 cm long when 5 N hangs on it and 30.0 cm long, when the weight is 10 N. What is the length of the spring if the weight is 3 N assuming Hooke's Law is obeyed?
Answer: D (23.0 cm)
The extra 5 N adds 5 cm, so the spring stretches 1 cm per newton and its natural length is 25 − 5 = 20 cm. With 3 N it is 23 cm.
The mass of a stone is 15.0 g when completely immersed in water and 10.0 g when completely immersed in a liquid of relative density 2.0. The mass of the stone in air is
Answer: C (20.0 g)
Loss in the liquid is twice the loss in water: m − 10 = 2(m − 15), so m = 20 g.
In which of the following is surface tension important?
Answer: B (The floating of a dry needle in water)
A dry needle is denser than water but is held up by the stretched surface film of the water, which is surface tension. Ships and balloons float by upthrust.
A thermometer with an arbitrary scale, S, of equal divisions registers −30°S at the ice point and +90°S at the steam point. Calculate the Celcius temperature corresponding to 60°S.
Answer: D (75.0°C)
θ = (60 − (−30))/(90 − (−30)) × 100 = 90/120 × 100 = 75°C.
A brass rod is 2 m long at a certain temperature. What is the length for a temperature rise of 100 K, if the expansivity of brass is 18 × 10−6 K−1?
Answer: A (2.0036 m)
Increase = 2 × 18 × 10−6 × 100 = 0.0036 m, giving 2.0036 m.
What is the difference in the amount of heat given out by 4 kg of steam and 4 kg of water when both are cooled from 100°C to 80°C? [The specific latent heat of steam is 2,260,000 J kg−1, specific heat capacity of water is 4200 J kg−1 K−1]
Answer: C (9,040,000 J)
Both give out the same heat cooling from 100°C to 80°C as water; the steam gives out extra latent heat when it condenses: 4 × 2 260 000 = 9 040 000 J.
The graphs below show the variation of volume (V) against temperature (T) in Kelvin for a given mass of gas at constant pressure. Which of the graphs depicts the behaviour of an ideal gas?
Answer: A (A)
Charles' law: at constant pressure V is proportional to the kelvin temperature, a straight line through the origin, as in A.
How long does it take a 750-W heater to raise the temperature of 1 kg of water from 20°C to 50°C. [Specific heat capacity of water = 4200 J kg−1 K−1]
Answer: C (168 s)
Heat needed = 1 × 4200 × 30 = 126 000 J. t = 126 000/750 = 168 s.
The absolute temperature of a perfect gas is proportional to the average
Answer: C (kinetic energy of the molecules)
Kinetic theory shows that the kelvin temperature of an ideal gas is proportional to the average kinetic energy of its molecules.
A room is heated by means of a charcoal fire. An occupant of the room standing away from the fire is warmed mainly by
Answer: B (radiation)
Heat reaches someone standing to the side of a fire mainly as radiation; convection currents carry warm air upwards.
A boy timed 30 oscillations of a certain pendulum thrice and obtained 1 min. 10 s, 1 min. 12 s and 1 min. 7 s respectively. The mean period of oscillation of the pendulum is
Answer: C (2.32 s)
Mean time for 30 oscillations = (70 + 72 + 67)/3 ≈ 69.7 s. Period = 69.7/30 ≈ 2.32 s.
Which of the following is TRUE of light and sound waves?
Answer: A (They both transmit energy)
All waves carry energy. Light needs no medium, sound is longitudinal, and light is about a million times faster.
The image in a pin-hole camera is
Answer: D (inverted and formed by the light from each point travelling in a straight line.)
Light from each point of the object travels in a straight line through the hole, so the top of the object is imaged at the bottom: the image is real and inverted.
When a plane mirror at which a ray is incident is rotated through an angle θ, the reflected ray will be rotated through
Answer: C (2θ)
Turning the mirror by θ turns the normal by θ, which changes both the angle of incidence and of reflection by θ, so the reflected ray turns through 2θ.
A trough 12.0 cm deep is filled with water of refractive index 4/3. By how much would a coin at the bottom of the trough appear to be displaced when viewed vertically from above the water surface?
Answer: A (3.0 cm)
Apparent depth = 12 ÷ (4/3) = 9 cm, so the coin seems raised by 12 − 9 = 3 cm.
In a ray diagram for a thin converging lens, a ray that is not parallel to the optic axis but passes through the optic centre will
Answer: A (pass through undeviated)
Near its centre a thin lens is like a thin parallel-sided slab, so a ray through the optical centre goes straight on.
Which of the following correctly describes the image of an object, 4 cm from a diverging lens of focal length −12 cm?
Answer: A (The image is virtual, 3 cm in front of the lens)
1/v = 1/f − 1/u = −1/12 − 1/4 = −1/3, so v = −3 cm: a virtual image 3 cm from the lens on the object's side.
Two tuning forks of frequencies 256 Hz and 260 Hz are sounded close to each other. What is the frequency of the beats produced?
Answer: B (4 Hz)
Beat frequency = difference of the two frequencies = 260 − 256 = 4 Hz.
A man hears his echo from a nearby hill 2 s after he shouted. If the frequency of his voice is 260 Hz and the wavelength is 1.29 m, how far away is the hill?
Answer: B (335.4 m)
v = fλ = 260 × 1.29 = 335.4 m s−1. The sound takes 1 s each way, so the hill is 335.4 m away.
When the bottom tip of a vibrating tuning fork is held in contact with a wooden box, a louder sound is heard. This phenomenon is known as
Answer: C (resonance)
The box is made to vibrate with the fork (forced vibration/resonance), so a bigger area moves the air and the sound is louder.
Which of the following statements is CORRECT about the earth's magnetic field?
Answer: B (The angle of declination is the angle between the magnetic meridian and the geographic meridian)
Declination is the angle between the magnetic meridian and the geographic meridian. Dip is measured from the horizontal, not the vertical.
The internal resistance of each of the cells E1 and E2 shown in the figure above is 2 Ω. Calculate the total current in the circuit.
Answer: C (0.40 A)
The two 2 V cells in parallel act as one 2 V cell of internal resistance 1 Ω. I = 2/(4 + 1) = 0.4 A.
The function of the system of granulated carbon mixed with manganese (IV) oxide in a Leclanche cell is to
Answer: C (prevent polarisation in the cell)
Manganese(IV) oxide is a depolariser: it removes the hydrogen that would collect on the carbon rod and polarise the cell.
A moving coil galvanometer of 300 Ω resistance gives full scale deflection for 1.0 mA. The resistance, R, of the shunt that is required to convert the galvanometer into a 3.0 A ammeter is
Answer: C (0.10 Ω)
The shunt carries 3 − 0.001 = 2.999 A at the meter's p.d. of 300 × 0.001 = 0.3 V. R = 0.3/2.999 ≈ 0.10 Ω.
Which of the following obeys Ohm's Law?
Answer: D (All metals)
Metals at constant temperature have a constant V/I. Glass is an insulator, and diodes and many electrolytes do not have a constant V/I.
The net capacitance in the circuit shown above is
Answer: D (2.0 μF)
The two 2 μF in parallel make 4 μF; in series with 4 μF: C = (4 × 4)/(4 + 4) = 2 μF.
An equipment whose power is 1500 W and resistance is 375 ohms would draw a current of
Answer: B (2.00 A)
P = I²R, so I = √(1500/375) = √4 = 2 A.
To convert an alternating current dynamo into a direct current dynamo, the
Answer: C (slip rings are replaced with a split ring commutator)
A split-ring commutator reverses the connections every half turn, so the output current always flows the same way.
If a current carrying coil is mounted on a metal frame, the back e.m.f. induced in the coil causes
Answer: B (eddy currents)
The changing magnetic flux also induces currents that circulate in the metal frame itself; these are eddy currents.
The electrochemical equivalent of platinum is 5.0 × 10−7 kg C−1. To plate-out 1.0 kg of platinum, a current of 100 A must be passed through an appropriate vessel for
Answer: A (5.6 hours)
t = m/(zI) = 1.0/(5.0 × 10−7 × 100) = 20 000 s ≈ 5.6 hours.
Which of the following statements are TRUE of isotopes? I. Isotopes of an element have the same chemical properties because they have the same number of electrons II. Isotopes of elements are normally separated using physical properties III. Isotopes of an element have the same number of protons in their nuclei.
Answer: D (I, II and III.)
Isotopes have the same number of protons and electrons, so they behave the same chemically; because of this they must be separated by physical methods that depend on their different masses (e.g. diffusion or a mass spectrometer). All three statements are true.
When an atom loses or gains a charge, it becomes
Answer: B (an ion)
An atom that has lost or gained electrons is charged and is called an ion.
4 g of a radioactive material of half-life 10 days is spilled on a laboratory floor. How long would it take to disintegrate 3.5 g of the material?
Answer: C (30 days)
0.5 g must remain: 4 → 2 → 1 → 0.5 g is three half-lives, 30 days.
In a nuclear fusion process, four protons each of mass Mp were fused to produce a nucleus X of mass Mx. Which of the following equations is CORRECT?
Answer: A (4Mp > Mx)
Fusion releases energy, which comes from a loss of mass, so the product is lighter than the four protons together.
Which of the following are TRUE for α-decay? I. Mass number decreases by four II. Atomic number decreases by two III. Mass number does not change
Answer: A (I and II only)
An alpha particle is 42He, so the nucleus loses 4 from its mass number and 2 from its atomic number.
Which of the following phenomena is called photoelectric effect?
Answer: C (A metal absorbs quanta of light and then emits electrons)
In the photoelectric effect a metal surface absorbs photons of light and gives out electrons. Option A describes X-ray production.