UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Show that Wien's law and Stefan-Boltzmann law are limiting cases of Planck's radiation law.

A plane electromagnetic wave is given by E_z = a \cos \omega x \cos \omega t and H_y = - a \sin \omega x \sin \omega t. Evaluate the instantaneous value of the Poynting vector \vec{S} and show that <\vec{S}> = 0.

When the current in an \text{R}-\text{L} circuit is decaying, what fraction of the original energy stored in the inductor has been dissipated after 2\cdot 3 time constant ?

With reference to ferromagnetic materials, explain the terms hysteresis and hysteresis loops.

In a double slit interference experiment, show that the fringe shape is a hyperbola.

Classify fibers based on the number of modes that can propagate through them. Depict step-index and graded-index multimode fibers pictorially.

Discuss the applications of lasers in communication and medicine.

Explain the lasing action of \text{He}-\text{Ne} laser using energy level diagram and describe the operation of \text{He}-\text{Ne} laser experimental set-up.

Discuss spatial evolution of Fresnel diffraction into Fraunhofer diffraction.

Consider a zone plate with radii r_n = 0\cdot 11 \sqrt{n}\text{ cm} illuminated by a monochromatic light of wavelength 589\text{ nm}. Calculate the positions of first two foci.

If a thin sheet of glass of thickness t and refractive index \mu is placed in the path of one of the interfering waves, show that the distance through which a fringe is displaced is a function of t.

A plano-convex lens of radius 1\cdot 0\text{ m} is placed on an optically flat glass plate. The space between the lens and the glass plate is filled with a liquid. The diameter of the 5^{\text{th}} ring changes to 3\cdot 0 \times 10^{-3}\text{ m}. Calculate the refractive index of the liquid when the ring is bright. The wavelength of light used is 589\text{ nm}.

A block of mass m is attached to one end of a combination of two massless springs connected in series. The other end of the combination is fixed to a rigid support. The spring constants of the two springs are k_1 and k_2, respectively. The block is free to move on a frictionless horizontal surface. If the block is pulled a little and then released, calculate the frequency of oscillation of the block.

An oscillator of mass 0\cdot 01\text{ kg} draws maximum power at a frequency of 96\text{ Hz} with half power points at 93\text{ Hz} and 99\text{ Hz}. If the amplitude of driving force is 3\cdot 88\text{ N}, calculate (i) quality factor, (ii) the damping factors and amplitude of the oscillator at resonance.

Write down the equation of motion of a weakly damped harmonic oscillator driven by a harmonic force. Obtain an expression for the maximum amplitude of oscillation under steady-state conditions.

A satellite revolves in a circular orbit around the Earth at a certain height above it. Calculate the time period of revolution of the satellite, if the radius of the Earth is significantly higher than the height at which the satellite revolves.

Obtain an expression for the angular speed of the Earth at which Coriolis force makes objects fly from its surface.

The above circuit exhibits a MOSFET with a source resistor. It has V_T = 1\text{ V} and \mu_n C_{ox} (W/L) = 2\text{ mA/V}^2. Calculate the drain voltage. Also determine whether the transistor is in saturation or in the triode region.

What is Meissner effect ? Determine the magnetic susceptibility of a superconductor. Explain whether a superconductor exhibits perfect ferromagnetism, paramagnetism or diamagnetism.

A type I superconductor with T_c = 7\text{ K} has slope \frac{dB_c}{dT} = -25\text{ mT/K} at transition temperature T_c. Estimate its critical field at 6\text{ K}.