UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What is the physical significance of Einstein's A-coefficient? Explain why it is more difficult to achieve Lasing action at X-ray wavelength than at infra-red wavelength.

In a certain engine, a piston undergoes vertical SHM with an amplitude of 10\,\mathrm{cm}. A washer rests on the top of the piston. As the motor is slowly speeded up, at what frequency will the washer no longer stay in contact with the piston?

Show that the group velocity is equal to particle velocity. Also prove that the group velocity of the photons is equal to c, the velocity of light.

A sphere of radius R moves with velocity \vec{u} in an incompressible, non-viscous ideal fluid. Calculate the pressure distribution over the surface of the sphere. Do you think that a force is necessary to keep the sphere in uniform motion?

A mirror is moving through vacuum with a relativistic speed v in the x-direction. A beam of light with frequency \omega_i is normally incident (from x=\infty) on the mirror.

(i) What is the frequency of the reflected light expressed in terms of \omega_i, c and v?

(ii) What is the energy of each reflected photon?

A body turns a fixed point. Show that the angle between its angular velocity vector and its angular momentum vector about a fixed point is always acute.

If I' and I be the Moments of Inertia of a body about an axis passing through an arbitrary origin and about a parallel axis through the centre of mass respectively, show that I' = MR^2 + I, where \vec{R} is the position vector of the centre of mass with respect to the arbitrary origin and M is the mass of the body.

Consider a rigid body rotating about an axis passing through a fixed point in the body with an angular velocity \vec{\omega}. Determine the kinetic energy of such a rotating body in a coordinate system of principal axis. If the earth suddenly stops rotating, what will happen to the rotational kinetic energy? Comment in detail.

Discuss the problem of scattering of charged particle by a coulomb field. Hence, obtain an expression for Rutherford scattering cross-section. What is the importance of the above expression?

A charged particle is moving under the influence of a point nucleus. Show that the orbit of the particle is an ellipse. Find out the time period of the motion.

The density inside a solid sphere of radius a is given by \rho = \frac{\rho_0 a}{r}, where \rho_0 is the density at the surface and r denotes the distance from the centre. Find the gravitational field due to this sphere at a distance 2a from its centre.

Explain how the circuit shown above can be a source of oscillations. Use this circuit to construct a transistor oscillator and explain its working. What is the frequency of oscillations of this circuit?

Construct a digital circuit to add three bits A, B and C and provide their sum and carry as outputs. Show appropriate Boolean expressions and truth table to justify the outputs.

Draw and explain the collector characteristics of a bipolar junction transistor in common emitter configuration. Using the plot, explain how the transistor can be used as an ON-OFF switch.

Starting with the expression for the density of states for electrons in a band, show that the Fermi energy of an intrinsic semiconductor is at the middle of the band gap. Use these results to estimate the electron density at 300 K (Assuming E_g=1\,\mathrm{eV} and the rest masses of electron and hole as m_e and m_h).

A perfect conductor and a superconductor with T_c \sim 10\ \mathrm{K} are subjected to the following conditions:

(i) cooled under applied magnetic field to 4\ \mathrm{K}

(ii) cooled to 4\ \mathrm{K} and then magnetic field is applied with schematic diagrams, explain path of magnetic field lines in all these situations.

Show that the London equation \vec{\nabla} \times \vec{J} = -\frac{1}{\mu_0\lambda_L^2}\vec{B} or \vec{j} = -\frac{c}{4\pi n\lambda_L^2}\vec{A} leads to the Meissner effect.

A crystal plane is shown in the above figure. Find its Miller indices and interplanar spacing.

Explain parity violation in \beta-decay. Describe how parity violation was experimentally detected in the decay of {}^{60}\mathrm{Co}. Mention any other decay process in which the parity violation has been demonstrated.

What is the role of neutrino in the weak interaction of radioactive nuclides? Explain the experimental detection of neutrino.