UPSC Physics Optional PYQs (CSE & IFoS)PYQs

In special theory of relativity, the Hamiltonian of a free particle with rest mass m_0 is given by \sqrt{p^2 c^2 + m_0^2 c^4}. Obtain the Lagrangian of the system using Legendre transformation.

Find the Boolean algebra expression for the above system.

What do you understand by spontaneous magnetization below Curie temperature ? Explain with an appropriate diagram, the occurrence of a hysteresis loop in a ferromagnetic material.

Determine the values of emitter current and the collector current of the transistor having \alpha = 0\cdot98 and collector to base leakage current I_\text{CBO} = 4\ \mu\text{A}. The base current is 50\ \mu\text{A}.

Define the terms critical magnetic field and critical temperature in a superconductor. Find the magnetic field strength necessary to destroy the superconductivity in a sample of lead at 4\cdot2\text{ K}. The critical magnetic field at 0\text{ K} is 0\cdot80\text{ Tesla} and the critical temperature is 7\cdot2\text{ K}.

Explain with the help of a neat diagram the working of an RC coupled common emitter amplifier.

Why does the resistance of a semiconductor decrease with increase in temperature ?

What is Meissner effect ? Explain perfect diamagnetism in reference to this.

Write down the semiempirical mass formula for nuclei and sketch the variation of isobaric masses with atomic number for both odd and even values of A. How many stable isobars would be there in each case ?

Predict the spin and parity for the ground state of the following nuclei on the basis of the shell model : {}_8^{15}\text{O}, {}_8^{16}\text{O}, {}_8^{17}\text{O}, {}_8^{18}\text{O}

Write the quark contents and the quantum numbers (B, J, s, I_3) of the following hadrons : \bar{\Sigma}^-, \Xi^\circ, \Pi^+, \bar{K}^\circ

Explain briefly SU(3) flavor symmetry and SU(2) isospin symmetry in particle physics.

Describe the main features of the shell model of the nucleus. Explain how it can account for the magic numbers of nuclei.

How much energy is required to separate {}_8^{16}\text{O} nucleus into its constituent nucleons ? What is the binding energy per nucleon for this nucleus ?

What are noncentral nuclear forces ? Discuss qualitatively how the presence of a small noncentral component in the nuclear force can account for the nonvanishing quadrupole moment of deuteron.

What is meant by quark confinement ? Why are the masses of hadrons larger than the sum of the masses of their constituent quarks ?

What are Stokes and anti-Stokes lines ? What is their importance in understanding the molecular structure ?

Consider two electrons system in (3p)^1(4s)^1 configuration. Derive the allowed energy states of the system in (i) LS coupling and (ii) jj coupling sketching the energy level diagram in each case. Name the interactions which are responsible for different splittings.

What is meant by Larmour precession ? Calculate the Larmour frequency for protons in a magnetic field of 1 Tesla.

The first rotational line in the rotational spectrum of CO is observed at 3\cdot84235\text{ cm}^{-1}. Calculate the rotational constant B and the bond length.