UPSC Physics Optional PYQs (CSE & IFoS)PYQs

At what temperature are the rates of spontaneous and stimulated emission equal? (Assume \lambda = 500\text{ nm})

Obtain an expression for the resolving power of a plane transmission grating. Deduce the missing orders for a double-slit Fraunhofer pattern, if the slit widths are 0\cdot 16\text{ mm} and 0\cdot 8\text{ mm} apart.

What are the important properties of a hologram?

For stationary waves on a string whose ends are fixed, show that the energy density is maximum at antinodes and minimum at nodes.

Show that the plane of polarisation is rotated through \theta = \frac{\delta}{2} = \frac{\pi d}{\lambda} (\mu_L - \mu_R) in optical rotation where symbols have their usual meanings.

Show that for any rigid body consisting of at least three particles, not arranged in one straight line, number of independent degrees of freedom is six. Define Euler's angles \theta, \phi and \psi to describe the configuration of such a rigid body. Consider two frames of reference, one fixed to the body and the other to the space defined as S' = (x', y', z') and S = (x, y, z) respectively. Show that the angular momentum (\vec{L}) of the rigid body in the two frames are related by \left( \frac{d\vec{L}}{dt} \right)_S = \left( \frac{d\vec{L}}{dt} \right)_{S'} + \vec{\omega} \times \vec{L} where \vec{\omega} is the angular velocity of rotation.

Show that the total energy per unit mass of liquid flowing from one point to another without any friction remains constant throughout the displacement.

Consider a spherical shell of mass M and radius R. Calculate the potential due to this shell at a point P when the point is (i) outside the shell and (ii) inside the shell (r < R). If the spherical shell is now replaced by a uniform solid sphere of same mass and radius, what will be its potential at the same external point?

Obtain the relativistic equation for aberration of light using velocity transformation equations.

Obtain Poiseuille's equation for a viscous fluid flowing through a narrow tube of radius r and length l. If a spherical body of radius a is allowed to move at a speed \vec{V} through the same fluid of viscosity \eta, show that the viscous force will increase with the speed linearly.

Show that a four-dimensional volume element dx\,dy\,dz\,dt is invariant to Lorentz transformation.

Two bodies of masses M_1 and M_2 are placed at a distance d apart. Show that at this position where the gravitational field due to them is zero, the potential is given by V = -\frac{G}{d} (M_1 + M_2 + 2\sqrt{M_1 M_2})

How can the NAND-gates be combined to perform the OR-operation ?

A certain colpits oscillator uses a tank circuit with L = 20\text{ mH}; C_1 = 200\text{ pf} and C_2 = 300\text{ pf}. What is the frequency of oscillation ?

Distinguish between 'soft' and 'hard' super-conductors. Explain how penetration depth varies with magnetic field strength and temperature.

Explain the switching action of a FET. Two JFETs are connected in parallel with \gamma_{d1} (drain resistance) = 20\text{ k}\Omega, \gamma_{d2} = 30\text{ k}\Omega and g_{m1} (transconductance) = 2\text{ m-mho} and g_{m2} = 4\text{ m-mho}. Find the efffective \gamma_d and g_m.

Draw the circuit diagram of a two-stage RC coupled common emitter transistor amplifier. Show how the magnitude and phase of voltage gain vary with frequency. Define bandwidth of this amplifier. An amplifier with open loop voltage gain, A_v = 1000 \pm 100 is available. It is necessary to have an amplifier whose voltage gain varies by no more than \pm 0.1\%. Find the reverse transmission factor \beta of the feedback network used and the gain with feedback.

Show that FCC-crystals are more closely packed than BCC-crystals,

(i) Transistors are current operated devices, while vacuum tubes are voltage operated." — Explain. (ii) Why are junction transistors called bipolar devices ?

Show the volt-ampere characteristics of a solar cell under illumination. Explain the characteristics.