45 questions. Try each one, then open the answer to check yourself and read the explanation.
When the base current of a common-emitter transistor is kept at zero, it operates in the
Answer: D (cut-off region.)
A transistor conducts only when a base current flows. With the base current at zero the collector current is (almost) zero, so the transistor is in the cut-off region (switched off).
One of the properties of gamma rays is that they are
Answer: C (neutral)
Gamma rays are electromagnetic waves (photons). They carry no charge and have no rest mass, so they are not deflected by electric or magnetic fields.
The theory of electronic conduction in solids, which satisfactorily explains the properties of conductors, insulators and semiconductors, is
Answer: B (band theory.)
Band theory explains conduction by the gap between the valence band and the conduction band: no gap in conductors, a small gap in semiconductors and a large gap in insulators.
A certain manufacturer wishes to make an n-type semi-conductor. Which materials would he select for dopping?
Answer: A (Arsenic and antimony)
n-type material is made by adding pentavalent (group V) atoms, which give a spare electron. Arsenic and antimony both have five valence electrons.
I. The number of neutrons released exceeds the number that caused the fission.
II. There is loss of mass.
III. Energy is produced
IV. Smaller nuclei merge to form larger nuclei.
Which of the statements above are correct about nuclear fission?
Answer: B (I, II and III only)
In fission a heavy nucleus splits, releasing more neutrons than it absorbed, with a loss of mass that appears as energy. Small nuclei joining together (IV) is fusion, so only I, II and III are correct.
The energy associated with the emitted photon when a mercury atom changes from one state to another is 3.3 eV. Calculate the frequency of the photon. [e = 1.6 × 10−19 C; h = 6.6 × 10−34 Js]
Answer: A (8.0 × 1014 Hz)
E = 3.3 × 1.6 × 10−19 = 5.28 × 10−19 J. f = E/h = 5.28 × 10−19 ÷ 6.6 × 10−34 = 8.0 × 1014 Hz.
A p-n junction diode is used as
Answer: C (a rectifier in an a.c circuit.)
A diode lets current flow in one direction only, so it is used to rectify (change a.c. to d.c.) in an a.c. circuit. It cannot amplify.
The battery connection that permits current to flow across a p-n junction is called
Answer: C (forward biased.)
When the p-side is connected to the positive terminal (forward bias), the depletion layer narrows and current flows across the junction.
The process through which free electrons leave the surface of hot metals is known as
Answer: A (thermionic emission.)
Heating a metal gives its free electrons enough energy to escape from the surface; this is thermionic emission.
A mirror of weight 75 N is hung by a cord from a hook on the wall. If the cord makes an angle of 30° with the horizontal, the tension in the cord is
Answer: A (150 N.)
The vertical part of the tension holds up the weight: T sin 30° = 75 N, so T = 75 ÷ 0.5 = 150 N.
The motion of smoke particles from a chimney is typical of
Answer: D (random motion.)
Smoke particles are knocked about irregularly by air molecules, so they move in no fixed direction: random motion.
The component of vector X along the direction of vector Y is zero when
Answer: D (X is perpendicular to Y.)
The component of X along Y is X cos θ. This is zero when cos θ = 0, that is θ = 90°, so X must be perpendicular to Y.
I. Work done by load is always less than the work done by effort
II. All machines are made of levers, pulleys, screws and gear wheels.
III. A fishing rod is a machine
IV. Effort is always larger than load.
Which of the statements above about machines are true?
Answer: C (I and III)
Friction makes useful work output less than work input (I true), and a fishing rod is a lever, so it is a machine (III true). Not all machines are levers, pulleys, screws or gears, and many machines lift a load bigger than the effort.
An engine of a car of power 80 kW moves on a rough road with a velocity of 32 ms−1. The force required to bring it to rest is
Answer: B (2.50 × 103 N.)
Power = force × velocity, so F = P/v = 80 000 ÷ 32 = 2500 N = 2.50 × 103 N.
If the radius of the earth is 6.4 × 106m, the escape velocity of a satellite from the earth is [g = 10ms−2]
Answer: C (1.13 × 104ms−1.)
Escape velocity v = √(2gR) = √(2 × 10 × 6.4 × 106) = √(1.28 × 108) ≈ 1.13 × 104 m s−1.
A shooter wants to fire a bullet in such a way that its horizontal range is equal to three times its maximum height. At what angle should he fire the bullet to achieve this?
Answer: A (53°)
R = 2u2sin θ cos θ/g and H = u2sin2θ/2g. Setting R = 3H gives 2 cos θ = 1.5 sin θ, so tan θ = 4/3 and θ ≈ 53°.
The correct unit of energy density is
Answer: B (kg m−1s−2.)
Energy density is energy per unit volume: J m−3 = (kg m2 s−2) ÷ m3 = kg m−1 s−2.
The production and type of charge of a body can only be accounted for by the
Answer: B (deficiency or surplus of electrons.)
Only electrons move when bodies are charged. A body with extra electrons is negative; one that has lost electrons is positive.
The electrolyte in the Nickel-iron (Nife) accumulator is
Answer: D (potassium hydroxide solution.)
The NiFe (alkaline) accumulator uses potassium hydroxide solution as its electrolyte; the lead-acid accumulator uses dilute sulphuric acid.
The main purpose of the transformer in an a.c. radio set is to
Answer: C (step down the voltage.)
A radio works on a low voltage, so its transformer steps the mains voltage down. A transformer cannot increase power or change a.c. to d.c.
When an a.c. voltage is applied to a capacitor, no power is consumed because the current
Answer: D (leads the voltage by 90°.)
In a pure capacitor the current leads the voltage by 90°, so the average power (VI cos 90°) is zero: energy stored in one quarter-cycle is returned in the next.
An electric heater with a p.d. of 240 V connected across its terminals has a total resistance of 960 Ω. Find the power rating of the heater.
Answer: C (60.00 W.)
P = V2/R = 2402 ÷ 960 = 57 600 ÷ 960 = 60 W.
An ammeter of resistance 5 Ω has a full-scale deflection when a current of 50 mA flows in it. The value of the resistor required to adapt it to measure a current of 5 A is
Answer: C (0.05 Ω)
A shunt in parallel must carry 5 − 0.05 = 4.95 A with the same p.d. as the meter: 0.05 × 5 = 4.95 × S, so S ≈ 0.05 Ω.
When a certain a.c. supply is connected to a lamp, it lights with the same brightness as it does with a 12 V d.c. battery. The r.m.s. value of the a.c. supply is
Answer: D (12.0 V.)
The r.m.s. value of an a.c. is the d.c. value that gives the same heating effect. Same brightness as 12 V d.c. means the r.m.s. voltage is 12 V.
If the capacitance of a capacitor is C = εA/d, which of the following parameters is varied when a variable capacitor is used for tuning radio sets?
Answer: A (Area and distance)
In a tuning capacitor, turning the knob moves one set of plates between the other, changing the overlapping area of the plates (and so the capacitance); the dielectric (air) stays the same.
Which of the following diagrams represents the magnetic field of two isolated unlike poles?
Answer: D (D)
Unlike poles attract, so field lines run straight across from N to S, and the arrows point from the N pole towards the S pole. Only D shows this.
A cell of internal resistance r is connected to an external resistor R. The condition for maximum power transfer is
Answer: C (R = r.)
The maximum power is delivered to the external resistor when its resistance equals the internal resistance of the cell: R = r.
The capacitance of a parallel-plate capacitor when in air is 3 μf and in the presence of a dielectric material 6 μf. The dielectric constant is
Answer: C (2.)
Dielectric constant = capacitance with dielectric ÷ capacitance in air = 6 ÷ 3 = 2.
A person can focus objects when they lie beyond 75cm from his eyes. The focal length of the lens required to reduce his least distance of distinct vision to 25 cm is
Answer: B (37.50 cm.)
This long-sighted person needs a converging lens that makes an object at u = 25 cm appear at 75 cm (virtual image, v = −75 cm). 1/f = 1/25 − 1/75 = 2/75, so f = 37.5 cm.
The frequency of the wave in the diagram above is
Answer: D (0.25 Hz.)
The graph completes one full cycle between t = 0 and t = 4.0 s, so the period T = 4 s and f = 1/T = 0.25 Hz.
An object placed 10 cm from a concave mirror of focal length 5cm would have its image
Answer: C (at the centre of curvature.)
The radius of curvature is 2f = 10 cm, so the object is at the centre of curvature. 1/v = 1/5 − 1/10 = 1/10 gives v = 10 cm: the image is also at the centre of curvature.
A progressive wave equation is represented by y = a sin (150 πt − πx/4). If the phase difference of a progressive wave is 45°, the value of x in the equation is
Answer: D (1 cm.)
The phase term is πx/4. A phase difference of 45° = π/4 rad, so πx/4 = π/4 and x = 1 cm.
Non-luminous objects can be seen because they
Answer: C (reflect light.)
Non-luminous objects do not give out their own light; we see them because they reflect light from a source into our eyes.
A submarine is observed to rise from a real depth of 80 m to 60 m in water. Calculate the change in apparent depth. [Refractive index of water = 4/3]
Answer: B (15m.)
Apparent depth = real depth ÷ n. 80 ÷ (4/3) = 60 m and 60 ÷ (4/3) = 45 m, so the apparent depth changes by 60 − 45 = 15 m.
The wavelength of the first overtone of a note in a closed pipe of length 33cm is
Answer: A (44cm.)
In a closed pipe the first overtone has L = 3λ/4, so λ = 4L/3 = 4 × 33 ÷ 3 = 44 cm.
The diagram above represents the stress-strain graph for a typical metal rod. What does X represent?
Answer: B (Breaking point)
The straight part ends at the proportional/elastic limit and the small dip is the yield point. The curve stops at X, where the rod breaks, so X is the breaking point.
If the relative density of gold is 19.2, the volume of 2.4 kg of gold is [Density of water = 103 kgm−3]
Answer: D (1.25 × 10−4 m3.)
Density of gold = 19.2 × 1000 = 19 200 kg m−3. Volume = mass ÷ density = 2.4 ÷ 19 200 = 1.25 × 10−4 m3.
The thermos flask is designed to
Answer: C (prevent heat loss or gain by conduction, convection and radiation.)
The vacuum, silvered walls and stopper cut down heat transfer in both directions, so a flask keeps hot things hot and cold things cold.
An immersion heater rated 2.0 A, 240 V is used to boil water from temperature 52°C to 100°C. If the mass of the water is 2.5 kg, determine the time taken to boil the water. [Specific heat capacity of water = 4.2 × 103 Jkg−1 K−1]
Answer: C (1.05 × 103s.)
Heat needed = mcΔθ = 2.5 × 4200 × 48 = 504 000 J. Power = IV = 2 × 240 = 480 W, so t = 504 000 ÷ 480 = 1050 s = 1.05 × 103 s.
What is likely to happen if the glass of a thermometer expands more upon heating than the liquid inside?
Answer: B (The liquid will go down in the stem)
If the bore of the glass grows faster than the liquid's volume, the liquid fills less of the tube, so its level falls in the stem.
A drop of petrol makes a finger colder than a drop of water would because
Answer: B (petrol takes its latent heat of vaporization from the finger.)
Petrol evaporates much faster than water, and the latent heat it needs to evaporate is taken from the finger, which cools it.
A uniform solid cube material 10 cm on each side of mass 700 g is submerged in water. Which of the following best describes the behaviour of the cube in water?
Answer: D (The cube will float)
Volume = 10 × 10 × 10 = 1000 cm3, so density = 700 ÷ 1000 = 0.7 g cm−3. This is less than water (1 g cm−3), so the cube rises and floats with 70% of it under water.
The thermometric property of a constant volume thermometer is
Answer: A (change in pressure.)
In a constant-volume gas thermometer the volume is kept fixed, and the gas pressure changes with temperature; pressure is the thermometric property.
At low humidity in an environment, the human skin is usually
Answer: D (dry and rough.)
When the air is dry, moisture evaporates quickly from the skin, leaving it dry and rough (cracked lips and skin in harmattan).
Atmospheric pressure = 76cm mercury
In the diagram above, the pressure of the gas is
Answer: B (86 cm of mercury.)
The mercury in the open limb stands 10 cm higher than on the gas side, so the gas pressure is atmospheric pressure plus 10 cm: 76 + 10 = 86 cm of mercury.