UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Show that the operator \left(\nabla^2-\frac{1}{c^2}\frac{\partial^2}{\partial t^2}\right) is invariant under Lorentz transformations.

A particle of rest mass M=4\times10^{-27}\ \mathrm{kg}, disintegrates into two particles of rest masses M_1=3\times10^{-27}\ \mathrm{kg} and M_2=1\times10^{-27}\ \mathrm{kg}. Show that the energies E_1 and E_2 of these two parts after disintegration satisfy the condition E_1=3E_2 while moving in opposite directions with equal linear momenta. Give necessary mathematical derivation.

A type I superconductor with T_c = 7\text{ K} has slope \frac{dB_c}{dT} = -25\text{ mT/K} at transition temperature T_c. Estimate its critical field at 6\text{ K}.

What is Meissner effect ? Determine the magnetic susceptibility of a superconductor. Explain whether a superconductor exhibits perfect ferromagnetism, paramagnetism or diamagnetism.

A power supply using a full-wave rectifier is to provide 100\text{ mA} at 20\text{ V} with no more than 1\% ripple. Calculate the minimum value of smoothing capacitor used. Consider the diode resistance and the resistance of the secondary of the transformer as negligible. Also take ripple frequency as 50\text{ cycles per second}.

For a simple cubic, a face centered cubic and a body centered cubic crystal, determine the atomic packing factor. How many atoms per \text{mm}^2 surface area are there in (100) plane for leads which has f.c.c. structure. The radius of the atoms is 0\cdot 174\text{ nm}.

Explain the race problem encountered in an RS latch and how it can be avoided. Build a Mod-10 counter using JK flip-flops and explain its working.

Construct an operational amplifier based analog computer to solve the differential equation \frac{d^2v}{dt^2}-\frac{dv}{dt}+2v=0.

What are the rules followed in biasing a bipolar junction transistor when it is used as an amplifier? Show how n-p-n and p-n-p transistors to be used as an amplifier are biased and the direction of flow of base, collector and emitter currents.

Starting from an expression for the group velocity, arrive at an expression for the effective mass of an electron in a semiconductor. Explain the significance of sign of the effective mass.

Explain the variation of Magnetisation of Type I and Type II superconductors as a function of applied magnetic field.

Classify diamagnetic, paramagnetic and ferromagnetic materials in terms of their magnetic susceptibility \psi. Plot and explain the variation of \frac{1}{\psi} with temperature for the three materials.

Metallic iron undergoes a structural phase transition from bcc to fcc at 910^\circ\mathrm{C}. At this temperature, the atomic radii of iron atoms in the bcc and fcc structures are 0.126 \times 10^{-9}\,\mathrm{m} and 0.129 \times 10^{-9}\,\mathrm{m} respectively. Calculate the volume change in percentage during this structural change.

(i) What is De Morgan's law ? (ii) Simplify the Boolean expression A + AB + ABC + ABCD

The above circuit exhibits a MOSFET with a source resistor. It has V_T = 1\text{ V} and \mu_n C_{ox} (W/L) = 2\text{ mA/V}^2. Calculate the drain voltage. Also determine whether the transistor is in saturation or in the triode region.

(i) Explain how the helicity of neutrino can be measured. (ii) What are 'strange particles' and what is 'strangeness number' ?

What are mirror nuclei? How does the charge independence of nuclear force emerges from this concept?

Write down the Bethe-Weizsäcker semiempirical mass formula for a nucleus. Explain the significance of each term occurring in it. Discuss the stability of a nucleus against \beta-decay. What is the effect of pairing term on stability?

Determine from the given data whether the following reactions are exothermic or endothermic:

(i) {}^{1}_{1}\mathrm{H}+{}^{3}_{1}\mathrm{H}\rightarrow{}^{2}_{1}\mathrm{H}+{}^{2}_{1}\mathrm{H}

(ii) {}^{12}_{6}\mathrm{C}+{}^{12}_{6}\mathrm{C}\rightarrow{}^{20}_{10}\mathrm{Ne}+{}^{4}_{2}\mathrm{He}

Calculate the recoil energy of {}^{57}_{26}\mathrm{Fe} nucleus when it emits a gamma photon of energy 14\,\mathrm{keV}.