UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Define Fermi energy. For an ideal Fermi gas of N particles at absolute zero temperature, show that the total energy of is 3/5 N E_F, where E_F is the Fermi energy.

Two bodies A and B have the same mass m each and are made of the same material with specific heat C per unit mass. A is at a temperature T and B is at a temperature 4T. What will be the entropy change of the universe when the bodies are brought into diathermic contact with each other?

Earth receives 1.3\text{KW/m}^2 of radiant energy from the Sun. Assuming Sun to be a spherical black body of radius 7 \times 10^8\text{m} and Earth-sun distance to be 1.5 \times 10^{11}\text{m}, Calculate the surface temperature of Sun. (Stefan-Boltzmenn constant \sigma = 5.67 \times 10^{-8}\text{ Wm}^{-2}\text{K}^{-4}).

Show that a sprining nucleus precesses in a magnetic field. Explain the underlying principle of NMR spectroscopy. The magnetic moment of a position is 2.793 \mu\text{ N}. Calculate the radio frequency at which nuclear magnetic resonance occurs in water kept in a magnetic field of T.

A plane wave of frequency \omega, which into two linear dielectric media. It has a normal incidence at the interface of the media. Giving appropriate for the intensities of reflected and transmitted rays.

Define Poynting vector and explain its significance. The electric field vector for an electromagnetic field travelling in vacuum is given by \vec{E} = E_0 \cos (kz - \omega t) \hat{i} Calculate the Poynting vector for the wave and show that its magnitude is equal to the energy density of the wave time the velocity of light.

A parallel LC circuit is operated at a frequency \omega, which is less than the resonant frequency \omega_0 of the LC circuit. Explain whether the reactance is inductive or capacitive.

What is Laplace equation ? Determine the average electric potential over a spherical surface, due to a point charge q placed at a distance r from the centre of the sphere. Assume r to be greater than the radius of the sphere.

Consider an infinite grounded conducting plane. If a point charge is held at a distanced d from the plane, compute by method of images, the electric potential above the plane and the induced charges on the conductor.

A cylinder of length L and radius b has its axis coincident with z-axis. The electric held in th region is E = 100 k. Find the electric flux through (i) the top circular end (ii) the bottom circular end (iii) the curved wall of the cylinder (iv) the closed surface of the cylinder

A bridge network with resistance, capacitance and inductance is given in the above figure. Show that the conditions for balancing the bridge are independent of the frequency of applied voltage.

How does Doppler effect of light of relativistic physics qualitatively differ from its non-relativistic analogue ? Calculate the Doppler shift in the frequency of a photon travelling along the y-axis. with respect to an observer moving along the x-axis with a constant speed v.

Two transverse harmonic waves, each of amplitude 5mm, wavelength 1m and speed 3 m/s are travelling in opposite directions along a stretched string fixed at both ends. Obtain an expression for the standing wave Produced. Locate the position at the nodes and antinodes.

Two thin convex lenses of focal length 0.2 m and 0.1 m are located 0.1m apart on the axis of symmetry. An object of height 0.1m is placed at a distance of 0.2 m from the first lens. Find by the matrix method, the position and the height of the image.

Explain the phenomenon of self focusing of laser beams.

Obtain an expression for the intensity of light in the Fraunhofer diffraction pattern due to a circular aperture. What is Airy pattern ? Explain with a neat diagram.

An ideal massless spring of force constant k has a mass m attached to one of its ends, the other and being fixed to a rigid support. The spring is horizontal floor, A resistive force -bv, proportional to the velocity v acts on the mass. Assuming the damping to be light, obtain the frequency of oscillation. When m = 0.1\text{ kg} and k = 10\text{ N/m}, it is found that the frequency of oscillation is \sqrt{1/2} times the frequency in the absence of damping. Calculate the value of the constant b.

Explain the phenomenon of pulse dispersion in a step index optical fibre.

What is holography ? Describe the experimental set up for Gabor's on-line holographic recording. What are the limitations of Gabors experiments? How these were over come by Leith and Upatneiks?

A block of mass m, attached to an ideal massless spring of force constant k, is at rest on a smooth horizontal floor. A second block of mass 2 m, moving with an initial velocity strikes the free end of the spring. The collision is one dimensional and elastic. (i) Calculate the maximum compression of the spring. (ii) What are the velocities of the block long time after the collision?