44 questions. Try each one, then open the answer to check yourself and read the explanation.
A man walks 1 km due east and then 1 km due north. His displacement is
Answer: C (√2 km N 45° E)
The two 1 km legs are at right angles, so the resultant is √(1² + 1²) = √2 km. Since both legs are equal, it points midway between north and east: N 45° E.
The frictional force between two bodies
Answer: E (has all of these characteristics.)
Friction appears only when there is motion or a tendency to move, it opposes that motion, it is proportional to the normal reaction and it hardly depends on the area of contact. All four statements are true.
An airforce jet flying with a speed of 335 m s−1 went past an anti-aircraft gun. How far is the aircraft 5 s later when the gun was fired?
Answer: D (1675 m)
Distance = speed × time = 335 × 5 = 1675 m.
A palm fruit dropped to the ground from the top of a tree 45 m tall. How long does it take to reach the ground? (g = 10 m s−2).
Answer: E (3 s)
Starting from rest, s = ½gt², so 45 = ½ × 10 × t², giving t² = 9 and t = 3 s.
A piece of rubber 10 cm long stretches 6 mm when a load of 100 N is hung from it. What is the strain?
Answer: C (6 × 10−2)
Strain = extension ÷ original length = 0.6 cm ÷ 10 cm = 0.06 = 6 × 10−2 (it has no unit).
An ice cube floats in a glass of water filled to the brim. What happens when the ice melts?
Answer: A (The water level remains the same)
A floating ice cube displaces its own weight of water. When it melts it becomes exactly that much water, which fills the space it was displacing, so the level does not change.
A machine gun with a mass of 5 kg fires a 50 g bullet at a speed of 100 m s−1. The recoil speed of the machine gun is
Answer: C (1 m/sec)
Momentum is conserved: 5 × v = 0.05 × 100 = 5, so the gun recoils at v = 1 m/s.
Mercury is a better barometric fluid than water because I. It needs no colouring II. Its density is many times greater than that of water III. It does not wet glass IV. It has a high vapour pressure V. It has a high boiling point. Which of the above statements are true?
Answer: B (I, II and III only)
Mercury is shiny and easy to see, it is about 13.6 times denser than water (so the column is short) and it does not wet glass. Its vapour pressure is low, not high, so IV is false; I, II and III are the reasons.
The internationally agreed system of units (SI) for physical measurements are
Answer: C (kg, m, sec)
The SI base units of mass, length and time are the kilogram, the metre and the second.
To determine the weight of an object you could
Answer: B (use a spring balance)
Weight is a force. A spring balance measures force directly, while a beam balance compares masses.
The force required to make an object of mass m, travelling with velocity v, turn in a circle of radius r is
Answer: A (mv2/r)
Circular motion needs a centripetal acceleration v²/r, so the force needed is F = mv²/r.
The density of a solid is defined as the
Answer: E (mass per unit volume of the solid)
Density = mass ÷ volume. Option A describes relative density, not density.
A solid suspended by a piece of string is completely immersed in water. On attempting to lift the solid out of the water, the string breaks when the solid is partly out of the water. This is because
Answer: C (the solid apparently weighs less when completely immersed in water than when partially immersed)
As the solid comes out of the water, less water is displaced, so the upthrust falls and the string must hold more of the weight. The tension is greatest when the solid is partly out, so the string breaks then.
The statements below were made by some students describing what happened during the determination of the melting point of solids. 1. The temperature of the solid was constant until melting started. 2. The temperature of the solid rose until melting started 3. During melting, the temperature was rising 4. During melting, the temperature was constant 5. The temperature continued to rise after all the solid had melted 6. The temperature stopped rising after all the solid had melted. Which of the following gives correct statements in the right order?
Answer: A (2, 4 and 5)
When a solid is heated its temperature rises up to the melting point (2), stays constant while it melts because the heat is used as latent heat (4), and then rises again once it is all liquid (5).
A few grains of table salt were put in a cup of cold water, kept at constant temperature and left undisturbed. Eventually all the water tasted salty. This action is due to
Answer: D (diffusion)
The dissolved salt particles spread out on their own from where they are concentrated to the rest of the water by random motion. This is diffusion.
A temperature of 20°C is the same as
Answer: B (68° F)
°F = (9/5 × °C) + 32 = 36 + 32 = 68°F.
The latent heat of fusion of ice is 80 cal g−1. How much heat is required to change 10 g of ice at 0°C into water at the same temperature?
Answer: D (800 cal)
Heat = mass × latent heat = 10 g × 80 cal g−1 = 800 cal.
A gas at pressure P N m−2 and temperature 27°C is heated to 77°C at constant volume. The new pressure is
Answer: C (1.16P N m−2)
At constant volume p/T is constant, with T in kelvin: p₂ = P × 350/300 ≈ 1.17P, closest to 1.16P.
The following are some units I. N s II. N m III. N m−2 IV. J °K−1 V. J kg−1. What are the units of latent heat?
Answer: E (V)
Specific latent heat is heat energy per unit mass, so its unit is joules per kilogram, J kg−1.
The heat from the sun reaches the earth by the process of
Answer: E (radiation)
Space between the sun and the earth is almost a vacuum, and only radiation can travel through a vacuum.
The amount of heat required to raise the temperature of a body is
Answer: E (thermal capacity.)
The heat needed to raise the temperature of a whole body by one degree is its thermal (heat) capacity; specific heat capacity refers to a unit mass.
Two lamps rated 40 W and 220 V each are connected in series. The total power dissipated in both lamps is
Answer: B (20 W)
Each lamp has resistance R = V²/P = 220²/40 = 1210 Ω, so in series on a 220 V supply the total resistance is 2420 Ω and the power is 220²/2420 = 20 W.
Two resistors R1 and R2 are connected in parallel, R2 being greater than R1. The combined resistance is
Answer: A (less than R1)
Adding a resistor in parallel gives the current an extra path, so the combined resistance is always less than the smallest resistor, R1.
Three 5 ohm resistors connected in parallel have a potential difference of 60 V applied across the combination. The current in each resistor is
Answer: C (12 A)
In parallel each resistor has the full 60 V across it, so I = V/R = 60/5 = 12 A.
If NEPA charges 5k per kWh, what is the cost of operating for 24 hours a lamp requiring 1 A on a 200 V line?
Answer: A (24K)
Power = IV = 200 W = 0.2 kW. Energy = 0.2 × 24 = 4.8 kWh, and 4.8 × 5k = 24k.
The equivalent capacitance for the circuit drawn below is
Answer: B (4 μF)
The 5 μF and 7 μF in parallel make 12 μF. That is in series with 6 μF: C = (6 × 12)/(6 + 12) = 4 μF.
A magnet is moved through a coil of wire. The e.m.f. produced in the wire depends on
Answer: D (all of the above)
By Faraday's law the induced e.m.f. equals the rate of change of flux linkage, which increases with more turns, a stronger magnet and faster motion.
In order to convert a galvanometer into an ammeter
Answer: A (a low resistance shunt is connected in parallel)
An ammeter must carry large currents, so most of the current is diverted through a low resistance (shunt) placed in parallel with the galvanometer.
In a D.C. circuit, a 10 microfarad (mf) capacitor is placed in series with a 10 ohm resistor. The total resistance of the combination is
Answer: E (infinite.)
Once charged, a capacitor lets no steady direct current through, so it acts like an infinite resistance in a d.c. circuit.
On an a.c generator, which of the following does not apply?
Answer: B (commutator)
An a.c. generator uses slip rings to collect alternating current. A commutator is used in a d.c. generator or motor.
Why is it impossible for the lines of force of an electric field to cross one another?
Answer: D (a positively charged particle can travel in only one direction at any time)
A line of force shows the direction a positive charge would move. If two lines crossed, the charge at that point would have two directions at once, which is impossible.
A potential difference of 6 V is used to produce a current of 5 A for 200 s through a heating coil. The heat produced is
Answer: E (6000 J.)
Heat = IVt = 5 × 6 × 200 = 6000 J.
The electric supply from Kainji Dam is transmitted at high voltages of the order hundreds of kilovolts but is converted to domestic use of about 220 volts by
Answer: E (transformers)
Alternating voltages are stepped down from transmission levels to 220 V by step-down transformers.
Every house supplied with electricity is provided with a box of fuses so that
Answer: C (the total current drawn from the mains can be limited)
A fuse melts and breaks the circuit when the current goes above its rating, so it limits the current drawn and protects the wiring.
An electric charge could be transmitted through
Answer: D (the human body, water and metals)
Charge flows through conductors. The human body, (impure) water and metals all conduct; wood, rubber, plastic, glass and cloth are insulators.
A guitar string is 75 cm long. The wavelength of its fundamental note is
Answer: B (150 cm)
In the fundamental mode the string is half a wavelength long: λ/2 = 75 cm, so λ = 150 cm.
Two boys are communicating with each other by stretching a string passing through a hole punched in the bottom of each of two tin cans. The physical principle employed is that sound travels
Answer: D (with greater ease through a string than in air)
The taut string carries the sound vibrations from one can to the other much better than the open air would.
A herdsman yelling out to fellow herdsman heard his voice reflected by a cliff 4 s later. What is the velocity of sound in air if the cliff is 680 m away?
Answer: C (340 m s−1)
The echo travels to the cliff and back, 2 × 680 = 1360 m, in 4 s, so v = 1360/4 = 340 m s−1.
An object 1 cm high placed on the axis 15 cm from a converging lens forms an image 30 cm from the lens. The size of the image is
Answer: E (2 cm.)
Magnification = v/u = 30/15 = 2, so the image is 2 × 1 cm = 2 cm high.
The visible part of light consists of the following colours:
Answer: B (red, green, blue, violet, indigo, orange and yellow)
Visible light is the seven colours red, orange, yellow, green, blue, indigo and violet. Infra-red and ultra-violet are invisible.
An object is positioned between two plane mirrors inclined at right angles to each other. The object is 1 unit distance from each mirror. The number of images formed is
Answer: C (3)
Number of images = 360°/θ − 1 = 360/90 − 1 = 3.
A string is sustaining a stationary wave when
Answer: C (two equal waves are travelling in opposite directions)
A stationary wave forms when two waves of the same frequency and amplitude travel in opposite directions and superpose, e.g. a wave and its reflection.
For the correction of myopic defects in the human eye we require
Answer: B (a concave lens)
A short-sighted (myopic) eye focuses distant light in front of the retina; a diverging (concave) lens spreads the rays so they focus on the retina.
Of the following which is different from the others?
Answer: C (cathode rays)
Cathode rays are streams of electrons (particles); the others are all electromagnetic waves.