UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What is meant by temporal and spatial coherence ? Show that the coherence length L = \lambda Q, where \lambda is the mean wavelength and Q represents the purity of a spectral line.

The potential energy for the interaction between two gas molecules can be represented by the function. \phi(r) = -\phi_0 \left[ 2 \left(\frac{r_0}{r}\right)^6 - \left(\frac{r_0}{r}\right)^{12} \right] Where \phi_0 and r_0 are constant. Prove that for small oscillations the frequency is given by \omega = \left( \frac{144 \phi_0}{m r_0^2} \right)^{1/2} Where m is mass of each molecule.

Write a short note on Fourier transformation.

Write the equation of motion for an oscillator driven by a simple harmonically varying force. Obtain the condition for maximum energy transfer to the oscillator.

A particle of mass m_1 moving with a velocity v_1 undergoes an elastic collision with a particle of mass m_2 at rest, in laboratory-frame. After the collision the first particle moves at a certain angle to the direction of its initial velocity, and this angle is \theta in laboratory-frame and \phi in centre of mass-frame. If the ratio of masses \left(\frac{m_2}{m_1}\right) is a, show that \theta and \phi are related as \tan \phi = \left(\frac{\sin \phi}{\cos \phi + \frac{1}{A}}\right).

A satellite has apogee and perigee heights above the sumace of earth as 4000 km and 640 km respectively. Calculate the eccentricity of the orbit and semi-major axis. Radius of the earth is 6400 km.

A spherical body of mass 'm' and radius 'a' is falling through a viscous fluid. If it started from rest and \eta is coefficient of viscosity of the fluid obtain an expression for its velocity as function of time. What is meant by relaxation time ? On what factors will it depend in this case?

A Particle of mass m, moving with an initial velocity v_0 is acted on by a central repulsive inverse-square force, F = \frac{k}{r^2}. Show that the scattering angle \phi depends on the impact parameter b as \cot \left(\frac{\phi}{2}\right) = \frac{m v_0^2}{k} b.

State Bernoulli's theorem. A horizontal pipe has a cross-section of 10\text{ cm}^2 in one region and 5\text{ cm}^2 in another. The pressure of water in the two regions is 2.370 \times 10^5\text{ N/m}^2 and 1.995 \times 10^5\text{ N/m}^2 respectively. Calculate the amount of water flowing through the pipe per minute.

Write a short note on Mass-energy equivalence.

The coordinates of an event in an inertial frame S are (25\text{ m}, 0, 0, 5 \times 10^{-8}\text{ s}). What will be the coordinates of this event in another interntial frame S' moving with a velocity 0.6 c in + x- direction with respect to S. The origins of the two frames were coincident at t = t' = 0

Define Coriolis force. Obtain an expression for the Coriolis force. How does it account for the whirling of winds in opposite directions in Northern and Southern hemispheres?

How does build in potential appear across a p-n junction? Explain under what biasing conditions drift and diffusion currents, respectively, dominate.

Draw the block diagram of a superhetro dyne radio receiver and explain the function of local oscillator.

Establish the two Barkhausen conditions for sustained sinusoidal oscillations. Sketch the circuit of Wien's bridge oscillator and explain its working.

Explain why even-even nuclei are more stable than odd-odd nuclei.

State conservation laws obeyed by strong and weak interactions.

Explain the orgin of anti-Stokes lines in Raman spectra.

What is space quantisation? Discuss the Stern Gerlach experiment establishing the space quantisation.

What are the term symbols of 2 equivalent p electrons? Write down the term symbols in ascending order of energies.