PYQ Bank

Define coefficients of viscosity and kinematic viscosity of a fluid. What are Poise and Stokes?

Using Poiseuille's formula, show that the volume of a liquid of viscosity coefficient \eta passing per second through a series of two capillary tubes of lengths l_1 and l_2 having radii r_1 and r_2 is obtained as Q=\frac{\pi p}{8\eta\left[\frac{l_1}{r_1^4}+\frac{l_2}{r_2^4}\right]}. where p is the effective pressure difference across the series.

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?

Show that the differential scattering cross-section can be expressed as \sigma(\theta)=\frac{s}{\sin\theta}\left|\frac{ds}{d\theta}\right|, where s is the impact parameter and \theta is the scattering angle.

Draw a neat diagram to explain the scattering of an incident beam of particles by a centre of force.

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.

Show that the moment of inertia of a circular disc of mass M and radius R about an axis passing through its centre and perpendicular to its plane is \frac{1}{2}MR^2.

In a cubic unit cell, find the angle between normals to the plane (111) and (121).

An electric field of 100\ \mathrm{V/m} is applied to a sample of n-type semiconductor whose Hall coefficient is -0.0125\ \mathrm{m^3/coulomb}. Determine the current density in the sample assuming \mu_x = 0.36\ \mathrm{m^2\,V^{-1}\,s^{-1}}.

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).

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 ?

Explain the working of SEM and TEM and highlight the major differences in principles. Draw neat schematic diagrams.

How does the energy gap in superconductors differ from the energy gap in insulator? How does it vary with temperature for superconductors?

Lead in the superconducting state has critical temperature of 6.2\ \mathrm{K} at zero magnetic field and a critical field of 0.064\ \mathrm{MA\,m^{-1}} at 0\ \mathrm{K}. Determine the critical field at 4\ \mathrm{K}.

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.

Show that the NAND gate is a universal gate.

For the logical equation given below, form the truth table and draw the corresponding logic circuit using different gates : Y = A \cdot B + \overline{A \cdot B}

The velocity of sound in f.c.c. gold and f.c.c. copper is 2100\,\mathrm{m/s} and 3800\,\mathrm{m/s} respectively. If the Debye temperature of copper is 348\,\mathrm{K}, then determine the Debye temperature of gold. Take the densities of gold and copper as 1.93 \times 10^{4}\,\mathrm{kg/m^3} and 0.89 \times 10^{4}\,\mathrm{kg/m^3} respectively.