UPSC Physics Optional PYQs (CSE & IFoS)PYQs

1 kg of ice at 0^\circ\text{ C} is melted and converted to water at 0^\circ\text{ C}. Compute the change in entropy.

Use the Maxwell relation \left(\frac{\partial s}{\partial v}\right)_T = \left(\frac{\partial p}{\partial T}\right)_v to show that the internal energy, U, of a thermodynamic system depends on the volume according to the expression \left(\frac{\partial U}{\partial v}\right)_T = T\left(\frac{\partial p}{\partial T}\right)_v - p where the symbols have their usual meanings. Use this result to derive Stefan's law for a black-body radiator.

Two point charges each of magnitude +2\text{ millicoulomb} are at A and B in front of a infinite conducting plane which is grounded. The line OAB is the perpendicular to time plane with the point O on the plane. If \mathrm{OA}=1\text{ m} and \mathrm{OB}=2\text{ m} calculate the force on the charge at A

Three point charges are situated at the vertices of an equilateral triangle (one at each vertex); Show that the electric intensity vanishes at the centroid if and only if the charges are equal in magnitude and of the same sign.

Write a short note on Wien's Law.

Write down Maxwell's equations in vacuum. Show that in the source-free case, both the electric and magnetic vectors obey wave equations of identical form and considering a plane wave solution, prove dial the electric and magnetic vectors and the direction of propagation are mutually perpendicular. Show further that there is a propagation of energy given by the Poynting vector.

A wire of length l is bent into the form of a rectangle of side a and b and carries a current I. Calculate the magnetic field intensity at the centre of the rectangle. Show further that the intensity is minimum for a = b.

An electromotive force p_0 \sin pt + E_1 \sin 2 pt is impressed on a circuit containing an inductor and a resistor. Set up the differential equation obeyed by the current and show that in the steady state the current comprises two sinusoidal terms. Calculate the average power dissipation in the circuit. What is the difference, if any, between a varying current and an alternating current?

Write a short note on Phase and Group velocities.

Write a short note on Rayleigh criterion for resolution.

Write a short note on Fraunhofer diffraction by circular aperture.

In double-slit Fraunhofer diffraction calculate the fringe spacing on a screen 50 cm away from the slits, if they are illuminated with blue light (\lambda = 4800\text{ \AA}), slit separation d=0.10 mm, and slit-width a=0.020 mm. What is the linear distance from the central maximum the First minimum of the fringe-envelope?

A movable bridge divides sonometer wire into two parts, which differ in length by 1.0 cm and produce 4 beats pre second when sounded together. If the whole length of the wire is 100 cm, find the frequencies of the parts.

How can it be proved experimentally that energy transmission is associated with a wave? The disc of a siren having 60 holes makes 420 revolutions per minute. Find the wavelength of its sound in air 0^\circ\text{C}, if velocity of sound at 0^\circ\text{C} is 332\text{ ms}^{-1}.

For transverse waves passing over a uniform string, prove that the slope of the siring at any position x at a given time is numerically equal to the ratio of the particle speed at that position x and time to the wave speed over the string.

Distinguish between spatial and temporal coherence.

A beam of lineal polarised light is changed into circularly polarised light by passing it through a slice of double-refracting crystal 0.0030 cm thick. Calculate to difference in the two refractive indices of the crystal, assuming this to be minimum thickness that will produce the result, and that the wavelength is 6 \times 10^{-5}\text{ cm}.

Explain the Laser actions in

(i) Helium Neon Laser

(ii) Gas Laser

Define Coriolis force and write an expression for it. Through suitable examples, explain the way this force varies in different parts of the earth's surface and for different velocities of the concerned particle.

Write a short note on Mass-Energy equivalence.