UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Calculate the inertia tensor for a rigid body consisting of three particles of masses 3\text{ gm}, 1\text{ gm}, 2\text{ gm} located at (1, -1, 2)\text{ cm}, (1, 0, 2)\text{ cm}, (-2, 1, 0)\text{ cm} respectively.

In a reference frame S, an event 1 occurs at the origin at t = 0 and another event 2 occurs at x = 4000\text{ m} and time t = 5 \times 10^{-6}\text{ s}. Find the time interval between the events as registered by clock in a frame S' moving with speed v = 0 \cdot 6 \, c relative to S along the common X-X' axis, the origin coinciding at t = t' = 0\,.

A particle of mass m moves under the action of a central force whose potential is V(r) = Kmr^4 (K > 0). Calculate the kinetic energy for which the orbit will be circle of radius R, about the origin.

(i) The quantities of rotatory motion are analogous to those of translatory motion. Write the corresponding equations of translatory and rotatory motion. (ii) Describe the theorems of perpendicular and parallel axes in case of a plane lamina.

A hoop is rolling down on an inclined plane without slipping. Find its velocity at the bottom of the inclined plane.

Calculate the gravitational self-energy of the Earth. Given : Mass of Earth M_e = 6 \times 10^{24}\text{ kg} and the Radius of Earth R_e = 6\cdot4 \times 10^6\text{ m}

A particle of mass m moves under the action of a central force whose potential is V(r) = Kmr^4 (K > 0). Calculate the kinetic energy for which the orbit will be circle of radius R, about the origin.

Calculate the velocity of a particle having kinetic energy four times the rest mass energy.

Calculate the inertia tensor for a rigid body consisting of three particles of masses 3 gm, 1 gm, 2 gm located at (1, -1, 2)\text{ cm}, (1, 0, 2)\text{ cm}, (-2, 1, 0)\text{ cm} respectively.

What are the consequences of Lorentz transformations on length and time when observed from a frame moving at relativistic velocities ?

(i) Derive the expressions for gravitational potentials at a point (I) outside the spherical shell, (II) inside the spherical shell. (ii) Calculate the escape velocity of a body of mass 10\text{ kg} from the surface of Moon \left( g_{\text{Moon}} = \frac{1}{6} g_{\text{Earth}} \right). Mass of Moon = 7\cdot3 \times 10^{22}\text{ kg} Radius of Moon = 1\cdot7 \times 10^6\text{ m}

Why can Electron-Positron pair production through a high energy photon not take place in vacuum?

Compare the dependence of resistance on temperature of a superconductor with that of a normal conductor. Describe briefly the formation of Cooper pairs.

Explain the drawbacks of Einstein's theory of specific heat and how it was overcome by Debye.

What is Meissner effect? Show that the Maxwell's equation is in contradiction to the Meissner effect. What are the inferences from this contradiction?

Why NAND and NOR gates are called universal gates? Give the logic diagram, Boolean equation and the truth table of a X–OR gate.

Explain why Type-II superconductor is better than Type-I superconductor in the application of superconductor magnets.

Show that for an n-type semiconductor, the Fermi level lies midway between the donor states and the conduction band edge at low temperature (assuming E_v=0).

Considering atoms hard, uniform spheres, find the number of atoms per unit cell and packing fraction for simple cubic, bcc and fcc structures.

Describe briefly the functions of the basic segments of a microprocessor. Draw a block diagram of the registers in the 8085 microprocessor.