UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Derive the distribution law which explains the black body spectrum over the entire wavelength region. Using this relation determine the value of Wiens constant b.

Obtain the characteristic impedance of the vacuum. Derive the expression used.

Write down Maxwell's equations in free space and hence show that the phase velocity of the electromagnetic wave is equal to the velocity of light in free space.

Calculate the magnetic moment of a coil having 100 turns, each of area 10\text{ cm}^2 carrying a current of 1\text{ mA}, flowing for 1\text{ ms}. The coil is placed in a magnetic field of 0.5\text{ kg} which is perpendicular to the magnetic moment. Calculate the torque acting on the coil and the angular momentum transferred to it.

An alternating voltage, v = V_0 \sin (\omega t + \phi) is applied to a series RL circuit through a switch. Find the sum total of the transient and steady currents. Find the conditions when transient current becomes

(i) zero, and

(ii) maximum

Write a short note on Phase and group velocities in dispersive media.

A plane transmission grating has 6000 lines per cm. Determine the angular separation between the two lines of sodium of wavelengths 5896\text{ \AA} and 5890\text{ \AA} in the second order spectrum. If the width of the grating is 2.5\text{ cm}, will these lines be resolved?

Why does a soap film appear coloured when is viewed by reflected white light? A thin film is illuminated by sodium light of wavelength 5900\text{\AA}. Its refractive index is 1.42. Calculate its minimum thickness so that it appears dark in reflected light.

Give the concept of Fresnel's half period zones. Describe the salient features of Fresnel's diffraction pattern due to a straight edge, showing the intensity distribution. How are these features explained?

What is a quarter plate? A phase retardation plate of quartz has a thickness 0.1436\text{ mm}. Calculate the wavelength in visible region for which this plate will act as a quarter for plate. The refraction indices of quartz for ordinary and extraordinary rays are 1.5443 and 1.5533 respectively.

What is spatial coherence ? Considering Young's two slit experiment, prove that the distance between the slits must be sufficiently less than (\lambda/\theta) for obtaining fringes of good contrast. \lambda is the wavelength of light used and \theta is the angle subtended by the source at the slits.

The amplitude of damped oscillator of frequency 300\text{ Hz} reduces one-tenth of its initial amplitude after 3000 oscillations. Calculate the damping constant and the time in which its energy will reduce to one-tenth of its initial energy.

A 3 MW laser beam which has a diameter of 1\text{ cm} is foccussed by a lens of focal length 5\text{ cm}. The wavelength of laser is 10,000\text{ \AA}. Calculate the intensity of the focal plane of the lens.

Write a short note on He-Ne laser.

A uniform rope of mass M and length L is hanging from a rigid support. A transverse wave travels along the rope. Calculate the speed of the wave at a distance x from the free end the time taken by the wave to travel the whole length.

In a hydrogen atom for the 2\text{p} \to 1\text{ s} transition the probability per unit time is 6 \times 10^8\text{ s}^{-1}. Calculate the angular frequency of the emitted photons and the order of Einstein's coefficient \text{B}_{21}.

Write a short note on Coriolis force and its effects.

Write a short note on Motion of rocket.

In the ammonia molecule the three hydrogen atoms form an equilateral triangle. The distance between the centre of this triangle from each hydrogen atom is 0.939\text{ \AA}. The nitrogen atom is at the apex of the pyramid with the three hydrogen atoms forming the base. The distance between the hydrogen and nitrogen atoms is 1.014\text{ \AA}. Find the position of the centre of mass relative to the nitrogen atom.

The tides in oceans on Earth are produced by gravitational pull of the Sun and the Moon. The pull due to Sun is much greater than the pull due to Moon. Explain, why tides due to Sun are only about 0.4 times as high as that due to Moon. The mass of the Sun is 2 \times 10^7 times the mass of the Moon and the distance between Sun and Earth is 400 times the distance between Moon and Earth. The radius of the Earth is 6.4 \times 10^6\text{ m}.