UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Verify whether the electric potential V = 15 x^2 y z - 5 y^3 z satisfies Laplace's equation or not.

Viewing ionosphere as a dielectric medium of refractive index \mu = \sqrt{1 - \omega_p^2 / \omega^2}, \omega_p being known as the plasma frequency, determine the group velocity of a radio wave of frequency \omega = \sqrt{2}\omega_p.

Explain physically why dispersion is diminished in multimode parabolic-index fiber than in step-index fiber.

Deduce an expression for resolving power of a diffraction grating, explaining its meaning. What will be the value of the number of slits in the grating to resolve \text{D}_1 and \text{D}_2 lines of sodium in the first order, assuming \lambda and \Delta\lambda respectively as 600\text{ nm} and 0\cdot6\text{ nm}?

With a planoconvex lens of radius of curvature R resting on a plane glass surface, Newton's rings are observed with incident light of wavelength \lambda. Find the radii of m\text{th} order dark rings. What will be the colour of the innermost ring with white light illumination?

In Young's double-slit experiment, a thin mica sheet (refractive index = 1 \cdot 5) is introduced in the path of one of the beams. If the central fringe gets shifted by 0 \cdot 2\text{ cm}, calculate the thickness of the mica sheet. Assume separation between the two slits (d) and between slit and source (D) as d = 0 \cdot 1\text{ cm} and D = 50\text{ cm}.

Explain, with neat diagrams, what you mean by monochromatic spherical aberration with reference to paraxial focus, marginal focus and circle of least confusion.

Obtain the equation of motion of a simple pendulum using Lagrangian formalism. Hence, obtain expression for the angular frequency of a simple harmonic oscillator.

Explain the refractive index distribution for a graded index optical fiber given as \begin{aligned} n^2(r) &= n_1^2 \left[ 1 - 2\delta \left( \frac{r}{a} \right)^q \right], & r < a \\ &= n_1^2 [1 - 2\delta] = n_2^2, & r > a \end{aligned} with usual meaning of symbols. Sketch and name the above profiles with justification for q = 1, 2 and \infty.

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.

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.

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}.

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?

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.

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

Show that the NAND gate is a universal gate.

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 ?

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).

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

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.