UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Write a note on Predictions of general theory of relativity and their experimental verification.

Write a note on Coriolis force and its manifestations.

For an isotropic solid define Young's modulus of elasticity Y, coefficient of rigidity \eta and Poisson's ratio \alpha. Establish the relation. \sigma = \frac{Y - 2\eta}{2\eta}

Show that the kinetic energy T of relativistic particle moving with momentum p is T = P^2 / m + m_0 What m_0 its rest mass and m is its relativistic mass.

A muon (\mu meson) is for med high up in the atmosphere and travels towards the earth with a speed of 0.992\text{ c}. It decays af ter travelling a distance of 6.0\text{ km}. In what time does the muon decay as measured (i) by us and (ii) in its own frame of reference? What is the distance covered the muon in its own frame of reference?

A steel ball 1.00\text{ mm} in diameter falls at a constant speed of 0.176\text{ cm s}^{-1} in a large vessel filled with oil. Calculate the dynamic viscosity of the oil (Density of steel = 7,700\text{ kg/m}^3 density of oil = 900\text{ kg/m}^3).

Air is blown through a pipe AB, at a rate of 15\text{ litres per minute}. The area of cross-section at A is 2\text{ cm}^2 whereas at B it is 0.2\text{ cm}^2. A tube abc, containing some water, is connected as shown. Find the difference in height, \Delta h, between the levels of water in the tube abc.

A triode has a transconductance (g_m) of 1,600\text{ micromhos}. The following table gives two sets of the plate voltage (E_b), the grid voltage (E_c) and the plate current (I_b).

Define the terms amplification factor and plate resistance and calculate them for the above case.

Draw a complete circuit for common emitter (small signal) amplifier for low frequencies and explain briefly its working.

Explain, on the basis of bond structure, the behaviour of insulators and conductors. Describe the effect of adding donor or acceptor impurities on conduction in a semi-conductor. Explain the action of a p-n junction as a rectifier. \begin{aligned} \text{Mass of electron} &= 9.1 \times 10^{-31}\text{ kg} \\\\ 1\text{ a.m.u} &= 931\text{ MeV} \\\\ \text{Avogadro's numbers} &= 6.1 \times 10^{23}\text{ (gm-mole)}^{-1} \\\\ \varepsilon_0 &= 1/36\pi \times 10^{-9}\text{ f/m} \\\\ h &= 6.6 \times 10^{-27}\text{ erg sec} \\\\ c &= 3.0 \times 10^{10}\text{ cm/sec} \\\\ 1\text{ eV} &= 1.6 \times 10^{-19}\text{ erg} \\\\ &= 1.6 \times 10^{-19}\text{ joule} \end{aligned}

Give an account of the basic principles of radio transmission and reception. Detailed circuits are not necessary but schematic diagrams indicating functions of various units may be shown.

Distinguish between dia-, para- and ferromagnetism. Give an account of Weiss theory of ferromagnetism.

Which of the following reactions are forbidden and why? \begin{aligned} p &\longrightarrow n + e^+ + u_e \\\\ \pi^+ &\longrightarrow \mu^+ + u_\mu \\\\ \text{H}^2 &\longrightarrow \text{He}^3 + e^- + e \end{aligned}

The number of alpha particles emitted per gm of radium each second is 3.71 \times 10^{10}. Atomic weight of radium is 226. Calculate its half-life in years.

Give an account of Pauli's exclusion principle. Show how it leads to the building up of the Periodic Table of elements. The description must particularly emphasize shell structure and the placing of alkali metals, halogens and inert gases in the Periodic Table.

Write a brief note (about 200\text{ words}) on X-ray absorption edges.

Find the Fermi energy in eV of electrons in sodium({}_{11}^{23}\text{C Na}), given its density to be 0.97\text{ g cm}^{-3}. Treat the electrons as a free gas.

Construct solutions of Schrodinger equation for a particle moving the potential \begin{aligned} V(x) &= 0 & \text{for } x < 0 \\\\ &= V_0 & \text{for } x > 0 \end{aligned} Deduce the reflection coefficient for particles incident from left to right (i.e. from negative to positive x regions) with energy E > V_0. Do you expect any reflection for particles of same energy incident from right to left? Explain qualitatively.

The stopping potential for electrons emitted from a metal, due to photoelectric effect, is found to be 1\text{ volt} for light of 2,500\text{ Angstrom units}. Calculate the work function of the metal in electron volts.

Consider the following equation of state for a gas: P = \frac{RT}{v-b} - \frac{a}{Tv^{2}} where a and b are constants and other symbols have their usual meaning. Find the values of P_{c}, T_{c} and V_{c} in terms of a and h at the critical point.