40 questions. Try each one, then open the answer to check yourself and read the explanation.
A carpenter on top of a roof 20.0 m high dropped a hammer of mass 1.5 kg and it fell freely to the ground. The kinetic energy of the hammer just before hitting the ground is [g ≈ 10 ms−2]
Answer: A (300 J)
All the potential energy becomes kinetic energy: KE = mgh = 1.5 × 10 × 20 = 300 J.
A man standing on a lift that is descending does not feel any weight because
Answer: A (there is no reaction from the floor of the lift)
We feel our weight through the push (reaction) of the floor. If the lift falls freely, the floor pushes on the man with zero force, so he feels weightless even though gravity still acts.
The diagram above shows two vectors at right angles to each other. The value of the resultant vector is
Answer: D (10.0 N.)
For perpendicular vectors, resultant = √(6.02 + 8.02) = √100 = 10.0 N.
An object of mass 2 kg moves with a velocity of 10 ms−1 round a circle of radius 4 m. Calculate the centripetal force on the object.
Answer: A (50 N)
F = mv2/r = 2 × 102 ÷ 4 = 50 N.
If it takes an object 3s to fall freely to the ground from a certain height, what is the distance covered by the object? [g ≈ 10 ms−2]
Answer: A (45 m)
Starting from rest, h = ½gt2 = ½ × 10 × 32 = 45 m.
The diagrams above show the positions of a cone. The position which can be described as neutral equilibrium is represented as
Answer: C (Z only)
A cone lying on its side (Z) just rolls to a new position and stays there, so it is in neutral equilibrium. On its base (Y) it is stable; on its apex (X) it is unstable.
If a tube of small radius opened at both ends is placed in a liquid, the liquid will
Answer: A (fall below the liquid level if the liquid does not wet the glass)
A liquid that does not wet glass (like mercury) is depressed in a capillary tube, falling below the outside level. A wetting liquid (like water) rises.
I. Density of the liquid.
II. Depth below the surface of the liquid.
III. Surface area of the liquid.
In which of the statements above will pressure be dependent?
Answer: C (I and II only)
Pressure in a liquid is p = hρg: it depends on the depth h and the density ρ, but not on the surface area.
I. High thermal capacity.
II. High sensitivity.
III. Easy readability.
IV. Accuracy over a wide range of temperatures.
From the statements above, the qualities of a good thermometer are
Answer: B (II, III and IV)
A good thermometer should be sensitive, easy to read and accurate over a wide range. It should have a low thermal capacity so it does not change the temperature it is measuring.
A machine is used to lift a load of 20 N through a height of 10 m. If the efficiency of the machine is 40%, how much work is done?
Answer: D (500 J)
Useful work output = 20 × 10 = 200 J. Work put in = output ÷ efficiency = 200 ÷ 0.4 = 500 J.
Which of the following could be effectively used to reduce friction?
Answer: D (Grease.)
Grease is a thick lubricant that stays between moving surfaces and keeps them apart, reducing friction. Water, petrol and kerosene run off or evaporate.
A copper wire was subjected to a tensile stress of 7.7 × 107Nm−2. Calculate the tensile strain of the wire. [Young modulus = 1.1 × 1011Nm−2]
Answer: A (7.0 × 10−4)
Strain = stress ÷ Young modulus = 7.7 × 107 ÷ 1.1 × 1011 = 7.0 × 10−4.
An object weighs 22kg in water and 30kg in air. What is the upthrust exerted by the liquid on the object? [g ≈ 10 ms−2]
Answer: B (80 N)
Upthrust = apparent loss of weight = (30 − 22) kg × 10 = 80 N.
A block of aluminium is heated electrically by a 30 W heater. If the temperature rises by 10°C in 5 minutes, the heat capacity of the aluminium is
Answer: C (900 JK−1)
Heat supplied = Pt = 30 × 300 = 9000 J. Heat capacity = 9000 ÷ 10 = 900 J K−1.
A perfect emitter or absorber of radiant energy is a
Answer: D (black body.)
A black body absorbs all radiation falling on it and is also the best possible emitter of radiation.
The phenomenon that shows that increase in pressure lowers the melting point can be observed in
Answer: B (regelation.)
In regelation, a loaded wire presses on ice, lowering its melting point so the ice melts under the wire and refreezes above it.
Steam burn is more severe than that of boiling water because
Answer: D (steam possesses greater heat energy per unit mass.)
Steam at 100°C gives out its large latent heat of vaporisation as it condenses on the skin, on top of the heat boiling water would give, so it burns more.
Which of the following types of waves needs a medium for preparation?
Answer: C (Sound waves.)
Sound is a mechanical wave and needs a material medium to travel. Radio waves, X-rays and light are electromagnetic and can cross a vacuum.
The ground is always cold at night because the
Answer: D (earth radiates heat to the atmosphere at night.)
At night the ground keeps losing heat by radiation but receives none from the sun, so it cools down.
I. Change of state II. Diffusion III. Radiation IV. Osmosis.
Which of the processes above can be explained using the kinetic theory?
Answer: B (I, II and IV)
Change of state, diffusion and osmosis all come from the motion of molecules, as the kinetic theory describes. Radiation is energy carried by electromagnetic waves, not by moving molecules.
When the human eye loses its power of accommodation, the defect is known as
Answer: D (presbyopia.)
With age the eye lens stiffens and can no longer change shape to focus near objects. This loss of accommodation is presbyopia.
A length of wire has a frequency of 255 Hz when stretched by a force of 225 N. If the force increases to 324 N, what is the new frequency of vibration?
Answer: C (306 Hz)
f ∝ √T, so f2 = 255 × √(324/225) = 255 × 18/15 = 306 Hz.
Which of the following electromagnetic waves has the highest frequency?
Answer: B (X-rays.)
In the electromagnetic spectrum the order of increasing frequency is radio, infrared, visible, ultraviolet, X-rays, gamma rays. Of the options, X-rays are highest.
The eclipse of the sun occurs when the
Answer: C (moon is between the sun and the earth)
A solar eclipse happens when the moon passes between the sun and the earth and blocks the sun's light from part of the earth.
A cannon is fired from town X. After how long is the sound heard at a town Y 4.95 km away? [Velocity of sound in air = 330ms−1]
Answer: B (15s)
Time = distance ÷ speed = 4950 ÷ 330 = 15 s.
An image in a convex lens is upright and magnified 3 times. If the focal length of the lens is 15 cm, what is the object distance?
Answer: C (10cm)
An upright image is virtual, so v = −3u. 1/u − 1/(3u) = 1/15 gives 2/(3u) = 1/15, so u = 10 cm.
The capacitance of a parallel plate capacitor is 20 μF in air and 60μF in the presence of a dielectric. What is the dielectric constant?
Answer: A (3.0)
Dielectric constant = capacitance with dielectric ÷ capacitance in air = 60 ÷ 20 = 3.0.
In the circuit above, three resistors, 2Ω, 4Ω and 12Ω are connected in parallel and a 12 V battery is connected across the combination. The current flowing through the 12Ω resistor is
Answer: D (1.0 A.)
Each resistor in parallel has the full 12 V across it, so the current in the 12 Ω resistor is 12 ÷ 12 = 1.0 A.
If the charge of electricity per kWh is ₦4, what is the cost of operating an electrical appliance rated 250 V, 2 A for 6 hours?
Answer: D (₦12)
Power = IV = 2 × 250 = 500 W = 0.5 kW. Energy = 0.5 × 6 = 3 kWh. Cost = 3 × ₦4 = ₦12.
The correct expression for the potential at a point, distance r from a charge q, in an electric field is
Answer: B (q/(4πε0r))
The potential of a point charge is V = q/(4πε0r). The expression with r2 is the electric field strength.
Three similar cells each of e.m.f 2 V and internal resistance 2Ω are connected in parallel, the total e.m.f and total internal resistance are respectively
Answer: D (2 V, 0.7Ω.)
Identical cells in parallel give the e.m.f. of one cell, 2 V, and an internal resistance of 2 ÷ 3 ≈ 0.7 Ω.
A radioactive isotope has a decay constant of 10−5s−1. Calculate its half life.
Answer: A (6.93 × 104s)
T½ = 0.693/λ = 0.693 ÷ 10−5 = 6.93 × 104 s.
Which of the following is a property of steel?
Answer: A (It can be used for making permanent magnets.)
Steel is hard to magnetise but keeps its magnetism for a long time, so it is used for permanent magnets. Soft iron is used for temporary magnets.
If the threshold frequency for tungsten is 1.3 × 1015 Hz, what is its work function? [h = 6.6 × 10−34 Js]
Answer: C (8.58 × 10−19J)
Work function W = hf0 = 6.6 × 10−34 × 1.3 × 1015 = 8.58 × 10−19 J.
In an a.c circuit, the ratio of r.m.s value to peak value of current is
Answer: A (1/√2)
For a sinusoidal a.c., Irms = I0/√2, so the ratio r.m.s. : peak = 1/√2 (about 0.707).
Under which of the following conditions do gases conduct electricity?
Answer: D (Low pressure and high p.d.)
Gases conduct when their pressure is low and a high p.d. is applied, as in a discharge tube.
In measuring high frequency a.c., the instrument used is the
Answer: B (hot wire ammeter)
A hot-wire ammeter works by the heating effect of the current, which does not depend on frequency, so it can measure high-frequency a.c.
The bond between silicon and germanium is
Answer: C (covalent)
Silicon and germanium atoms are held together by sharing pairs of valence electrons, which are covalent bonds.
Which of the following materials has an increase in resistance with temperature?
Answer: D (Metals.)
In metals the atoms vibrate more when heated and obstruct the free electrons more, so resistance rises with temperature.
The electrical properties of germanium can be altered drastically by the addition of impurities. This process is referred to as
Answer: B (doping.)
Adding small amounts of impurity atoms to a pure semiconductor to change its conductivity is called doping.