UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Starting from Biot-Savart law, calculate the magnetic field at the centre of a solenoid of length 1 meter, radius 2 cm and having 25 turns per centimeter, the current through the solenoid being 1 ampere.

The components of an electrostatic field in vacuo are given as E_x = \frac{a}{r^3} + \frac{bx^2}{r^5} E_y = \frac{cxy}{r^5} E_z = \frac{fxz}{r^5} where a,b,c, and f are constants x,y,z, the rectangular cartesian coordinates and r^2=x^2+y^2+z^2. Using the basic equations obeyed by the electrostatic field in vacuo, find he relations between a,b,c and f and determine the charge density at a general point in space. Would that explain the observed field?

A circular coil of wire having 100 turns and radius 10 cm is rotating about a vertical axis in its own plane uniformly at rate of 480 revolutions per minute. There is a horizontal magnetic field of intensity 0.01\text{ Wb/m}^2. The terminals of the coil are connected to the ends of an inductor having inductance 0.01 henry. Assuming that the resistance in the circuit can be neglected, find the current in the circuit at the instant the plane of the rotating coil is perpendicular to the magnetic field.

Define solar constant and say which of the values 1.34\text{ W/m}^2, 1.34 \times 10^3\text{ W/m}^2, 1.34 \times 10^5\text{ W/m}^2 is valid for it. Calculate the total energy radiated by the sun in one second and hence the decrease in its mass per second.

What is hologram? Explain how the image of the object is formed when one looks through it.

For a certain wave, system the angular velocity \omega and the wave vector k are related as follows: \omega = \omega_0 \left| \sin \frac{k a}{2} \right| \quad \text{for } -\frac{\pi}{a} < k < \frac{\pi}{a} Determine and plot the phase velocity and the group velocity for this system.

Two transverse sine waves each of amplitude 4\text{ mm} wavelength 2\text{m} and time period 1\text{ s} and in-phase at x=0, t=0 are travelling along the x-axis in opposite directions. Obtain the equation of the resultant wave and comment on its nature. Calculate the maximum displacement at x=2.3\text{ m}. Also locate the antinodes and nodes.

Nine Kilograms of mercury is poured into a glass U-tube of uniform internal diameter of 1.2\text{ cm}. It oscillates freely about its equilibrium position. Calculate the period of oscillation.

Write down the differential equation for a damped simple harmonic oscillator. Solve it and discuss the characteristics of dead-beat motion.

A single, slit of width 0.14\text{ mm} is illuminated normally by monochromatic light and diffraction bands are observed on a screen 2\text{ m} away. If the centre of the second dark band is 1.6\text{ cm} from the middle of the central bright band deduce the wavelength of light.

Show schematically the intensity distribution for a 2-slit Fraunhofer diffraction-interference, if slit-widths are 2\lambda each and centres of slits have separation 6\lambda. Assume incident light falling normally, and limit the discussion to the central diffraction band range.

Write a note on Ruby laser.

Explain mathematically how left and right circularly polarized light is produced by combining two linearly polarized beams. Given a beam of light, how can one experimentally test whether it is unpolarized or circularly polarized?

Write a note on Rayleighs criterion and resolving power of a telescope.

A pipe of varying diameter is used to lift water by 7\text{ m} the area of cross-section of the base is 125\text{ cm}^2 and the pressure here is 2.5 \times 10^5\text{ N/m}^2. The area of cross-section of the top is 25\text{ cm}^2. The rate of flow of water is 3 \times 10^{-2}\text{ m}^3/\text{s}. Calculate the pressure of water at the top neglecting energy losses.

Write a note on Experimental verification of variation of mass with velocity.

Prove the addition theorem of velocities in Special Theory of Relativity. Two bodies A and B are moving away in opposite directions each with a speed of 0.70\text{ c} with respect to a stationary observer. Deduce the speed or B as measured by A.

Write down Lorentz transformation relations and prove that x^2 + y^2 + z^2 - c^2 t^2 is invariant under this transformation. An event occurs at x^1 = 60\text{ m} at t^1 = 8 \times 10^{-8}\text{ s} in a reference frame S' which is moving along the common x or x' axis with a speed 3c/5 with reference to a stationary from S. The origins of the two frames coincide at t=0, t'=0. Deduce the space time coordinates of the event in the frame S.

Write a note on Gyroscope and its applications.

A thin uniform rod of length l and mass m is hinged to the floor at its lower end. It begins to fall from a vertical position. Deduce an expression for the angular speed of the road when it hits the floor. How would you explain that the rod would suffer less damage if the floor is soft than if the floor is hard?