UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A vacuum of the order of 10^{-11}\text{ cm of Hg} is obtained in the laboratory. Estimate the number of molecules of gas per cobic centimeter at 27^\circ \text{C} in that vacuum.

Using Maxwell's thermodynamic relations show that the internal energy of an ideal gas at a constant temperature is independent of its volume while for a real gas it is a function of Volume also.

State the principle of equipartition of energy. What are its limitations? Show that it is applicable only when the energy is a quadratic function of the associated variable.

What is Brownian motion? Deduce Einstein's formula for translatory Brownian motion of particles suspended in a liquid and hence determine the avogadro's number.

Write a short note on Specific heat of solids.

Show that attenuation constant \alpha and phase factor \beta for an electromagnetic wave, propagating in a perfectly conducting medium, are equal. At what frequency the skin depth in silver is 1\ \mu\text{m} when the conductivity of silver is 30 \times 10^6\text{ Siemens/meter} and relative permeability is 1.0?

Write a short note on Solar constant.

Starting from Biot Savart's law, find the vector potential at a distance r, from a current carrying wire.

A relay has a coil resistance of 10\ \Omega and inductance of 1\text{ H}. It is energized by a single voltage pulse of 10\text{ V} which remains constant for 250\text{ ms} and then falls to 0\text{ V}. Relay contact closes when the increasing current reaches 200\text{ mA} and opens when the decreasing current is at 100\text{ mA}. Calculate the time for which the relay contact is closed.

Self inductance of two coils, A and B, connected in series is 25\text{ mH} or 10\text{ mH}, depending on the relative current directions in the coils. Self inductance of the isolated coil. A, is 10\text{ mH}. Calculate mutual inductance M of the pair of coils coupling factor and leakage factor. If the current in coils is changing at the rate of 1000\text{ A/s}, find the induced electromotive forces across the coil A.

An electric dipole moment, \vec{p}_2, is placed at (r, \theta) in he electric field of another dipole moment \vec{p}_1, placed at he origin. Assuming that the electric potential, V, at (r, \theta) due to \vec{p}_1 is V(r, \theta) = \frac{p_1 \cos \theta}{4 \pi \epsilon_0 r^2} find the dipole-dipole interaction energy.

An alternating voltage is applied to the circuit shown in Fig. 1. Show that it has two resonant frequencies, f_p and f_s interrelated as f_p = f_s \sqrt{\left(1 + \frac{1}{r}\right)} Where r = \left(\frac{C_b}{C_a}\right)

Show that electromagnetic propagating in a homogeneous isotropic medium, arc transverse in nature.

Obtain an expression for the ratio of the probabilities of stimulated and spontaneous emissions. What do you infer from this relation? How is population inversion interpreted thermodynamically?

Describe the working principle of a three level solid state laser giving the transitions involved in the laser action.

Write a short note on Holography.

What is a quarter wave plate? Explain its use in the production and detection of circularly polarized light. For calcite for \lambda = 5472 \text{\AA}, \mu_O = 1.658 and \mu_E = 1.486. If the minimum thickness of a plate that can be cut from calcite is 30 \mu\text{ m}, what should be the minimum thickness for preparing a quarter wave plate?

A fine slit is illuminate by monochromatic light of wave-length 6000 Å. A thin wire is placed parallel to the slit and the diffraction pattern is observed on a screen at a distance of 1 m from the wire. In the shadow of the wire equidistant fringes of thickness 1.5 mm are observed. How do you explain this observation ? Calculate he diameter of the wire also.

The angular separation between two distant stars is 1 arc-second. If the effective wavelength of light is 5500 Å; what should be the diameter of the objective of a telescope so that the stars are just resolved?

Show that the interference fringes obtained in Young's two slit experiment are hyperbolic in shape. Under what conditions these are expected to appear straight?