Physics: previous-year questions

Answer: (A) $50h$

The energy of a photon is given by Planck's relation $E = h\nu$, where $\nu$ is the frequency. Putting $\nu = 50$ Hz gives $E = 50h$ joules, option A. Option C is the trap: $E = \frac{hc}{\lambda}$ is the form of the same relation in terms of wavelength, so $\frac{hc}{50}$ would be right only if 50 were the wavelength in metres; options B and D are dimensionally wrong. Facts to remember: $h = 6.626 \times 10^{-34}$ J s, photon energy rises with frequency (gamma rays highest, radio waves lowest), and 50 Hz is also the frequency of India's AC mains supply.

Answer: (B) 15-20%

Answer as of 2024 — this may have changed since.

Ordinary commercial solar panels made of crystalline silicon convert roughly 15 to 20% of the sunlight falling on them into electricity (the best current modules reach a little over 22%), so option B is the accepted range. A single-junction silicon cell cannot exceed about 33% in theory (the Shockley-Queisser limit); efficiencies above 40% have been reached only by multi-junction cells in laboratories and on satellites, and 80 to 90% is impossible for photovoltaics. Solar cells work on the photovoltaic effect and are made mainly of silicon, a semiconductor. Related facts: the International Solar Alliance is headquartered at Gurugram, and India aims at 500 GW of non-fossil power capacity by 2030.

Answer: (A) zero

Work done is $W = Fs\cos\theta$, where $\theta$ is the angle between the force and the displacement. In a circular orbit the gravitational pull acts along the radius towards the Sun while the planet moves along the tangent, so $\theta = 90^\circ$ at every instant and the work done is zero over any part of the path, including half the circumference. That is also why the planet's speed and kinetic energy stay constant in a circular orbit. Options B, C and D wrongly multiply the force by the path length or the diameter. General rule: a centripetal force never does work. (In an elliptical orbit gravity does work over parts of the path, but the total over one full revolution is still zero.)

Answer: (D) Silicon

Silicon is a semiconductor: its conductivity lies between that of conductors and insulators and rises with temperature or when small amounts of impurities are added (doping). Germanium is the other elemental semiconductor; both belong to Group 14 and are metalloids, while gallium arsenide is a compound semiconductor. Doping with phosphorus or arsenic gives n-type and with boron or aluminium gives p-type material, the basis of diodes, transistors, integrated circuits and solar cells. Iron and zinc are ordinary metallic conductors, and mercury, the only metal that is liquid at room temperature, also conducts electricity.

Answer: (D) Thorium

India has small uranium reserves but some of the world's largest reserves of thorium, found in the monazite sands of the Kerala, Tamil Nadu, Odisha and Andhra Pradesh coasts. Thorium-232 is 'fertile': in a reactor it absorbs a neutron and turns into fissile uranium-233. Homi Bhabha's three-stage nuclear programme is built around this: Stage 1, pressurised heavy water reactors using natural uranium; Stage 2, fast breeder reactors using plutonium (Kalpakkam); Stage 3, thorium-based reactors. Actinium and neptunium are scarce radioactive elements not available in quantity, and copper is not a nuclear fuel. Uranium is mined at Jaduguda (Jharkhand) and Tummalapalle (Andhra Pradesh).

Answer: (C) low pressure and high temperature.

An ideal gas is assumed to have molecules of negligible volume with no forces between them. A real gas comes closest to this at low pressure, when the molecules are far apart, and at high temperature, when they move too fast for intermolecular attraction to matter, so option C is correct. The opposite conditions, high pressure and low temperature (B), are exactly those used to liquefy gases, where deviation from ideal behaviour is greatest. The ideal gas equation is $PV = nRT$; real gases are described by the van der Waals equation $\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$, in which $a$ corrects for intermolecular attraction and $b$ for molecular volume.

Answer: (A) $\frac{1}{10}\ \Omega$ cm

Resistance $R = \rho \frac{L}{A}$, so resistivity $\rho = \frac{RA}{L}$. Working in centimetres, $L = 1$ m $= 100$ cm and $A = 1\ \mathrm{cm^2}$: $\rho = \frac{10 \times 1}{100} = \frac{1}{10}\ \Omega$ cm. The trap is to forget the conversion of 1 m into 100 cm, which gives $10\ \Omega$ cm (option C). In SI units the answer is $10^{-3}\ \Omega$ m. Resistivity depends only on the material and its temperature, not on the length or thickness of the wire; its reciprocal is conductivity. Silver has the lowest resistivity among metals, and alloys such as nichrome, with high resistivity, are used in heating elements.

Answer: (B) weight

The poundal is the absolute unit of force in the FPS system (the force that gives 1 lb an acceleration of 1 ft/s²). Weight is a force, so of the options given it is the quantity measured in poundals. Mass is measured in pounds, momentum in lb·ft/s and energy in foot-poundals, so A, C and D are wrong.

Answer: (A) shortsightedness

If the eye lens becomes too strongly converging (higher power), distant objects are focused in front of the retina, which is myopia or shortsightedness. Longsightedness is caused by too little converging power, astigmatism by an unevenly curved cornea, and colour blindness by defective cone cells.

Answer: (A) Steel

Steel has high retentivity and high coercivity, so once magnetised it keeps its magnetism, which is what a permanent magnet needs. Soft iron loses its magnetism easily and is used for electromagnets, copper is not ferromagnetic, and nickel is only weakly suited compared with steel.

Answer: (C) both (A) and (B)

A moving charge (an electric current) produces a magnetic field, and by Maxwell's displacement-current idea a changing electric field also produces one. Since both sources work, the answer is (C); choosing only (A) or (B) leaves out the other.

Answer: (D) Black

The sky looks blue from the ground because air molecules scatter blue sunlight towards us. In outer space there is no atmosphere to scatter light, so the sky appears black. Red, blue and indigo would all require scattering by air.

No option is correct as printed — this question is disputed. WBPSC awarded the mark to all candidates: two options (B) 380–750 nm and (C) 390–700 nm are both standard textbook ranges for the visible spectrum.

The question has more than one defensible answer: the limits of visible light are quoted variously as about 380–750 nm and about 390–700 nm (roughly 400–700 nm), so both (B) and (C) appear in standard books. The PSC therefore awarded the mark to all candidates.

Answer: (A) decreased

In an adiabatic process no heat enters or leaves, so by the first law $\Delta U = -W$. During expansion the gas does work on its surroundings, so its internal energy falls and it cools. It cannot increase or stay the same, and 'dissipated' is not the right description.

Answer: (B) Current density

Current density $\vec{J}$ (current per unit area) has a direction at each point and is a vector. Electric current, though it has a sense of flow, does not obey vector addition and is a scalar; power and wattless current are also scalars.

Answer: (C) Copper

In a metal such as copper, resistance rises with temperature because the vibrating lattice scatters electrons more, giving a positive temperature coefficient. Carbon and the semiconductor germanium have negative coefficients, and electrolytes conduct better when warmed.

Answer: (C) 2f

Kinetic energy depends on $v^2$, and $\sin^2\omega t = \frac{1 - \cos 2\omega t}{2}$, so the kinetic and potential energies oscillate at twice the pendulum's frequency, 2f. Kinetic energy peaks twice per oscillation (once each way through the mean position), so f or f/2 is wrong.

Answer: (B) Lenz's Law.

Lenz's law states that the induced e.m.f. acts in a direction that opposes the change in flux causing it, so it gives the direction. Faraday's law gives the magnitude of the induced e.m.f., and Ampere's and Maxwell's laws relate currents and fields.

Answer: (B) increases

Charge of either sign spreads over the bubble's surface, and the like charges repel each other, producing an outward electrostatic pressure. This adds to the gas pressure inside, so the bubble expands and its radius increases; the sign of the charge does not matter.

Answer: (A) Angular acceleration

The rotational form of Newton's second law is $\tau = I\alpha$, so a constant torque produces a constant angular acceleration. Angular velocity and displacement then change over time as a result, and linear acceleration needs a net force rather than a torque.