PYQ Bank

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.

Write a short note on Specific heat of solids.

Explain the concept of entropy The specific heat C_p of a material depends on temperature T according to the relation: C_p = a + bT + cT^2 \text{ where a, b and c are constants,} Derive an expression for the change in its entropy when the temperature changes from T_1 to T_2.

How is absolute scale of temperature obtained with the help of Carnol cycle? Hence define absolute zero

To what extent the pressure in a cathode ray tube must be reduced so that 90\% of the electrons emitted by the cathode reach the anode which is at a distance of 20\text{ cm} from the cathode? The mean molecular radius of main constituent gases of atmosphere is 2\text{\AA} and the number of molecules at standard pressure (760\text{ mm of Hg}) is 3 \times 10^{25} per \text{m}^3.

Write a short note on Solar constant.

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?

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

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.

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

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)

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.

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.

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.

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?

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

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?

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

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