UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Write down precisely the conservation theorems for energy, linear momentum, and angular momentum of a particle with their mathematical forms.

Show that the moment of inertia of a circular disc of mass M and radius R about an axis passing through its centre and perpendicular to its plane is \frac{1}{2}MR^2.

Solve Euler's equation of motion for a rigid body to show that the torque-free motion of a spherical top is a uniform rotation about an axis fixed in space.

Find the velocity and momentum of a particle having rest mass m_0 and kinetic energy equal to two times of its rest mass energy.

A particle of mass m is moving with the velocity \vec{v} on the surface of the earth. Discuss the nature of its motion in both the hemispheres due to the Coriolis force \vec{F} = -2\,m\,\vec{\omega} \times \vec{v}.

Describe briefly the Michelson-Morley experiment and discuss the significance of its null result in the context of the special theory of relativity.

The Lagrangian for a particle has the form L = \frac{1}{2} m (\dot{x}^2 + \dot{y}^2) - U(r) Obtain its form in plane polar coordinates and then get expression for the Hamiltonian using appropriate transformation.

Discuss that the motion of a particle in a central field gets restricted to a plane provided its angular momentum is nonzero. What will happen if the angular momentum is zero?

In a cubic unit cell, find the angle between normals to the plane (111) and (121).

Explain the working of SEM and TEM and highlight the major differences in principles. Draw neat schematic diagrams.

The velocity of sound in f.c.c. gold and f.c.c. copper is 2100\,\mathrm{m/s} and 3800\,\mathrm{m/s} respectively. If the Debye temperature of copper is 348\,\mathrm{K}, then determine the Debye temperature of gold. Take the densities of gold and copper as 1.93 \times 10^{4}\,\mathrm{kg/m^3} and 0.89 \times 10^{4}\,\mathrm{kg/m^3} respectively.

What is the reciprocal lattice and why is it named so? Derive the relationships for the primitive translation vectors of the reciprocal lattice in terms of those of the direct lattice.

An electric field of 100\ \mathrm{V/m} is applied to a sample of n-type semiconductor whose Hall coefficient is -0.0125\ \mathrm{m^3/coulomb}. Determine the current density in the sample assuming \mu_x = 0.36\ \mathrm{m^2\,V^{-1}\,s^{-1}}.

Lead in the superconducting state has critical temperature of 6.2\ \mathrm{K} at zero magnetic field and a critical field of 0.064\ \mathrm{MA\,m^{-1}} at 0\ \mathrm{K}. Determine the critical field at 4\ \mathrm{K}.

A silicon diode operates at a forward bias voltage of 0\cdot 4\text{ V}. Calculate the factor by which the current will be multiplied when the temperature is increased from 25^\circ\text{C} to 150^\circ\text{C} (\eta for \text{Si} = 2).

For the logical equation given below, form the truth table and draw the corresponding logic circuit using different gates : Y = A \cdot B + \overline{A \cdot B}

X-ray of wavelength 1\cdot 4\text{ \AA} is found to be Bragg reflected from (111) plane of an fcc structure. If the lattice parameter of the crystal is 5\text{ \AA}, find the angle at which the X-ray beam is incident on the (111) plane of the crystal.

What is ac Josephson effect ? Derive an expression for the current flowing through the junction formed by two superconducting films separated by an insulator.

Explain with the help of a neat diagram the structure of a n-channel FET and its IV characteristics. In what way is an FET different from a BJT ?

Show that the NAND gate is a universal gate.