48 questions. Try each one, then open the answer to check yourself and read the explanation.
The refractive index of the medium M in the diagram above is
Answer: D (√3)
The ray meets the surface at 30°, so the angle of incidence is 60°; inside M it makes 60° with the surface, so the angle of refraction is 30°. n = sin 60° ÷ sin 30° = √3.
What types of mirrors are capable of producing parallel beams of light such as those arising from the headlamps of a car?
Answer: B (parabolic mirrors)
A lamp at the focus of a parabolic mirror sends out a parallel beam; a spherical mirror only does this roughly.
A person can focus an object only when it lies within 200 cm from him. Which spectacles should be used to increase his maximum distance of distinct vision to infinity?
Answer: A (concave lens)
He is short-sighted (far point 200 cm). A diverging (concave) lens makes rays from distant objects seem to come from within his far point.
In which of the following material media would sound travel fastest?
Answer: C (metal)
Sound travels fastest in solids such as metals, where particles are closely bound, and slowest in gases.
Calculate the angle of minimum deviation for a ray which is refracted through an equiangular prism of refractive index 1.4.
Answer: A (29°)
n = sin((A + D)/2) ÷ sin(A/2): sin((60 + D)/2) = 1.4 × 0.5 = 0.7, so (60 + D)/2 = 44.4° and D ≈ 29°.
What happens to the rays in a parallel beam of light?
Answer: B (they meet at infinity)
Parallel rays never come together at any finite distance; in optics we say they meet at infinity.
If u is the object distance and v the image distance, which of the following expressions gives the linear magnification produced by a convex lens of focal length f?
Answer: C (v/f − 1)
From 1/u + 1/v = 1/f, multiplying by v gives v/u + 1 = v/f, so m = v/u = v/f − 1.
A ray of light makes an angle of 35° with a plane mirror. What is the angle of reflection?
Answer: A (55°)
Angles are measured from the normal: 90° − 35° = 55° is the angle of incidence, and the angle of reflection equals it.
The pitch of a sound note depends on
Answer: D (frequency.)
Pitch is how high or low a note sounds, and it is set by the frequency.
If the angle between two vectors P and Q is 0°, the vectors are said to
Answer: B (be parallel.)
An angle of 0° between two vectors means they point in the same direction: they are parallel.
A machine whose efficiency is 60% has a velocity ratio of 5. If a force of 500N is applied to lift a load P, what is the magnitude of P?
Answer: D (1500N)
MA = efficiency × VR = 0.6 × 5 = 3, so P = 3 × 500 = 1500 N.
A body of mass 4kg is acted on by a constant force of 12N for 3 seconds. The kinetic energy gained by the body at the end of the time is
Answer: A (162J.)
a = 12/4 = 3 m s−2, v = 3 × 3 = 9 m s−1, KE = ½ × 4 × 92 = 162 J.
As the pressure of a fluid increases, its viscosity
Answer: D (increases.)
Squeezing a liquid packs its molecules closer, so it resists flow more: viscosity increases with pressure.
I. Jet-propelled aircraft II. Rocket propulsion III. The recoil of a gun IV. A person walking
Which of the above is based on Newton's third law of motion?
Answer: A (I, II, III and IV)
All four are action–reaction pairs: jets and rockets push gas backwards, a gun pushes the bullet forwards, and a walker pushes the ground backwards.
In a hydraulic press, a force of 40N is applied on the effort piston of area 0.4m2. If the force exerted on the load piston is 400N, the area of the large piston is
Answer: B (4m2.)
Pressure is the same on both pistons: 40/0.4 = 400/A, so A = 4 m2.
A 100kg box is pushed along a road with a force of 500N. If the box moves with a uniform velocity, the coefficient of friction between the box and the road is
Answer: A (0.5.)
Uniform velocity means friction equals the push: μ = 500 ÷ (100 × 10) = 0.5.
The earth is four times the size of the moon and the acceleration due to gravity on the earth is 80 times that on the moon. The ratio of the mass of the moon to that of the earth is
Answer: B (1:1280.)
g = GM/R2, so M ∝ gR2. Mmoon/Mearth = (1/80) × (1/4)2 = 1/1280.
The diagram above shows forces 4N, 6N, 10N and 8N which act at a point O in the directions indicated. The net horizontal force is
Answer: D (13N)
The 8 N and 6 N forces each make 60° with the horizontal, so their horizontal parts are 8 cos 60° = 4 N and 6 cos 60° = 3 N. Net = 10 + 4 + 3 − 4 = 13 N.
A radioisotope has a decay constant of 10−7s−1. The average life of the radioisotope is
Answer: C (1.00 × 107s.)
The average (mean) life is 1/λ = 1/10−7 = 1.00 × 107 s. (0.693/λ would be the half-life.)
A moving-coil galvanometer has a full-scale deflection of 3A equivalent to 30° deflection. The sensitivity of the instrument is
Answer: A (10.0.)
Sensitivity is deflection per unit current: 30° ÷ 3 A = 10° per ampere.
In a tuned radio receiver R, L, C series circuit for resonance, the inductive and capacitive reactance XL and XC respectively are related as
Answer: C (XL = XC)
At resonance the inductive and capacitive reactances are equal and cancel, so the impedance is just R.
The particle and wave nature of matter are demonstrated in the equation
Answer: A (λ = h/p)
de Broglie's equation λ = h/p links a wave property (wavelength) to a particle property (momentum).
For semiconductors to have negative temperature coefficient of resistance implies that
Answer: D (their resistance decreases with temperature.)
A negative temperature coefficient means resistance falls as temperature rises.
Fluorescent tubes produce light by the
Answer: B (excitation of gas molecules.)
Electrons excite the gas (mercury vapour) atoms; as they return to lower levels they emit radiation that makes the coating glow.
In a reverse biased junction diode, current flows in by
Answer: C (minority carriers.)
Reverse bias blocks the majority carriers; the tiny leakage current is carried by minority carriers.
The energy stored in an inductor of inductance 5mH when a current of 6A flows through it is
Answer: D (9.0 × 10−2J.)
E = ½LI2 = ½ × 5 × 10−3 × 62 = 9.0 × 10−2 J.
X-rays can be used in the study of crystal structures because they
Answer: A (have an extremely short wavelength.)
X-ray wavelengths are about the same as the spacing of atoms in a crystal, so crystals diffract them.
An a.c. circuit of emf 12V has a resistor of resistance 8Ω connected in series to an inductor of inductive reactance 16Ω and a capacitor of capacitive reactance 10Ω. The current flow in the circuit is
Answer: C (1.2A.)
Z = √(82 + (16 − 10)2) = 10 Ω, so I = 12/10 = 1.2 A.
A generator-manufacturing company was contracted to produce an a.c dynamo but inadvertently produced a d.c. dynamo. To correct this error, the
Answer: A (commutator should be replaced with slip rings.)
A d.c. dynamo uses a split-ring commutator; replacing it with slip rings gives alternating current.
Transverse waves can be distinguished from longitudinal waves using the characteristics of
Answer: B (polarization.)
Only transverse waves can be polarized; all waves show reflection, refraction and diffraction.
A man exerts a pressure of 2.8 × 103 Nm−2 on the ground and has 4 × 10−2m2 of his feet in contact with the ground. The weight of the man is
Answer: A (112 N.)
Weight = pressure × area = 2.8 × 103 × 4 × 10−2 = 112 N.
When left in a freezer, a bottle full of water cracks on freezing into ice because of the
Answer: D (increase in the volume of water.)
Water expands when it freezes, so the ice takes more space than the water and breaks the bottle.
The change in volume when 450kg of ice is completely melted is [density of ice = 900 kgm−3, density of water = 1000 kgm−3]
Answer: A (0.05m3.)
Volume of ice = 450/900 = 0.50 m3; volume of water = 450/1000 = 0.45 m3; change = 0.05 m3.
If a force of 50N stretches a wire from 20m to 20.01m, what is the amount of force required to stretch the same material from 20m to 20.05m?
Answer: C (250N)
By Hooke's law force ∝ extension: 0.05 m is 5 times 0.01 m, so F = 5 × 50 = 250 N.
Tea pots are often silver-coated to prevent heat loss by
Answer: B (radiation only.)
A shiny silver surface is a poor emitter of radiation, so it cuts heat loss by radiation.
The phase difference between waves P and Q in the diagram above is
Answer: C (π/4)
Q's crests lag P's by about one-eighth of a wavelength; one full wavelength is 2π, so the phase difference is 2π/8 = π/4.
Metal rods of length 20m each are laid end to end to form a bridge at 25°C. What gap will be provided between consecutive rails for the bridge to withstand 75°C? [Linear expansivity of the material = 2.0 × 10−5 K−1]
Answer: C (0.02m)
Expansion = αLΔθ = 2.0 × 10−5 × 20 × 50 = 0.02 m, so the gap must be 0.02 m.
A 50W electric heater is used to heat a metal block of mass 5kg. If in 10 minutes a temperature rise of 12°C is achieved, the specific heat capacity of the metal is
Answer: A (500 J kg−1K−1)
Pt = mcΔθ: c = 50 × 600 ÷ (5 × 12) = 500 J kg−1 K−1.
I. Wavelength II. Medium of propagation III. Wave velocity IV. Frequency V. Energy
Which of the above are used for characterizing waves?
Answer: D (I, III and IV)
A wave is described by its wavelength, frequency and speed (linked by v = fλ); the medium and energy do not characterise it.
The instrument used for securing a large number of similar charges by induction is called
Answer: B (electrophorus.)
The electrophorus can be charged by induction again and again from one charged plate, giving many similar charges.
If 16mA of current flows through a conductor in one second, the number of electrons transported per second is [1 electronic charge = 1.6 × 10−19C]
Answer: B (1.00 × 1017.)
n = It/e = 16 × 10−3 × 1 ÷ 1.6 × 10−19 = 1.0 × 1017.
The difference between x-rays and gamma rays is that
Answer: A (x-rays arise from energy changes in the electronic structure of atoms while gamma rays come from the nucleus.)
Both are electromagnetic waves; X-rays come from electron energy changes in atoms, gamma rays from the nucleus.
In the diagram above, the ratio of the electric power dissipated in the 6Ω and 3Ω resistors respectively is
Answer: B (1:2.)
Both resistors have the full 12 V across them. P = V2/R gives 24 W and 48 W, a ratio of 1 : 2.
To protect a material from the influence of an external magnetic field, the material should be kept in a
Answer: D (soft iron ring.)
Soft iron is very permeable, so the field lines pass through the ring instead of the space inside it (magnetic shielding).
Which of the following is an electrolyte?
Answer: A (grape juice)
Grape juice contains acids and salts that form ions, so it conducts and is decomposed by current; the others do not ionise.
Electrical appliances in homes are normally earthed so that
Answer: B (a person touching the appliances is safe from electric shock.)
If a fault makes the casing live, current runs to earth (and blows the fuse) instead of through the person.
A cell whose internal resistance is 0.5Ω delivers a current of 4A to an external resistor. The lost voltage of the cell is
Answer: D (2.000V.)
Lost volts = Ir = 4 × 0.5 = 2 V.
Given three capacitors 0.3μF, 0.5μF and 0.2μF, the joint capacitance when arranged to give minimum capacitance is
Answer: C (0.1μF.)
Minimum capacitance is in series: 1/C = 1/0.3 + 1/0.5 + 1/0.2 ≈ 10.3, so C ≈ 0.1 μF.