UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A volume of one gm-mole of an ideal gas expands isothermally to four times its initial volume. Calculate the change in its entropy in terms of gas constant.

A gas possesses a Maxwellian velocity distribution function. Show that the fraction of molecules in a given volume that possess a velocity (+v_x) in one direction only and whose magnitude is greater than some selected value v_o is \int_{v_o}^{\infty} f(V_x) dv_x = \frac{1}{2} \left[ 1 - \frac{1}{\sqrt{\pi}} \text{erf} \left( \frac{1/4 m v_o^2}{KT} \right)^{1/2} \right] Symbols have their usual meanings.

Find the temperature at which root mean square velocity of nitrogen molecules in earth’s atmosphere equals the velocity of escape from the earth’s gravitational field. Mass of N_2 atom = 23.24 \times 10^{24}\text{ g}. Mean radius of earth = 6370\text{ km}.

Write a short note on Negative temperature.

A singly charged positive ion is accelerated through a potential difference of one \text{kV}, and the ion passes through a uniform magnetic field of B=0.2\text{ Wb/m}^{2} and consequently gets deflected through a circular path of radius 0.1\text{ metre}. Find out the mass number of the ion.

Write down the expression for energy distribution of a black- body radiation at temperature T and deduce Wien’s displacement law.

Derive an expression for the Poynting's vector and explain us significance A light source (one kilowatt) is radiating energy uniformly. Determine the intensity of the electric field at a distance of one metre from the sources.

State Kirchoff's laws for the distribution of currents (a) in the usual form for steady currents and (b) in a form applicable to alternating current networks. Discuss the method for comparing inductances by using Maxwell's bridge. State the disadvantages of the method.

Discuss briefly the various ways of modulation of electromagnetic waves for the purpose of communication through radio and television.

A 220\text{ volt}, 50\text{ cycle}, supply is connected to a circuit containing a resistance of 20\text{ ohms} in series with a 100\mu\text{F} capacitor. Determine the current and the phase.

The above expression shows that, for given W, \theta and \lambda, the resolving power is independent of number of grooves on the grating. Why do most diffraction gratings have several hundred grooves per mm?

Write a short note on Holography.

A beam of linearly polarised light is changed into circularly polarised light by passing it through a slice crystal 0.003\text{ cm} thick. Calculate the difference in refractive index of two rays in crystal assuming this to be minimum thickness that will produce the effect and that the wavelength of light is 6 \times 10^{-7}\text{ m}.

Show that the resolving power of a diffraction grating used with light of wavelength \lambda at normal incidence is W \sin \theta/\lambda, where W is the total width of the grating \theta the angle of diffraction.

The diameter of the central zone of a zone-plate is 2.3\text{ mm}. If a point source of light (\lambda=589.3\text{ nanometer}) is placed at a distance of 6\text{ metre} from it, calculate the position of the first image.

Write a short note on Spatial and temporal coherence.

A thick wire of mass per unit length m, density p, and Young’s Modulus E, is stretched between two supports and has a tension T. Obtain from first principles an expression for the velocity of longitudinal waves in the wire. Write down the equivalent expression for velocity of transverse waves in the same wire.

Calculate the rate of energy dissipation by a damped harmonic oscillator, in the weak damping limit with \omega_o \tau \gg 1, so that \omega=\omega_o. Symbols have their usual meanings.

If two pipes one closed at one end and the other open at both ends, have fast overtones of the same frequency, what is the ratio of their respective lengths?

Two express trains travelling at 10\text{ km/hour} are meeting each other while one of them is whistling. If the frequency of the note is 800\text{ Hz}, find the apparent pitch as heard by an observer in the other train after they passed each other. Velocity of sound in air = 340\text{ ms}^{-1}.