UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What is the recoil energy in electron-volts of a nucleus of mass 10^{-23}\text{ gm} after emission of x-ray of energy 1\text{ MeV}?

What is the angular momentum (referred to the centre of the orbit) of a satellite of mass M, which moves round the earth in a circular orbit of radius r? The result is to be expressed in terms only r, G.M, and M_e (the mass of the earth).

Write a short note on Motion of rocket under constant force field.

Two objects (M_1=2\text{ gm}: M_2=5\text{ gm}) process Velocities V_1= 10\hat{x}\text{ cm/sec}, V_2 = 3\hat{x}+ 5\hat{y}\text{ cm/sec} just prior to a collision during which they become permanently attached to each other. What is the final momentum of combination of the laboratory system ?

Show from the Lorentz transformation that two events (t_1=t_2) at different points (x_1 \neq x_2) in reference frame S are not in general simultaneous in reference frame S which is moving in the + direction with the constant velocity V with respect to S.

What is the momentum of a proton having kinetic energy 1\text{ BeV} ? The energy equivalent to proton rest mass is 0.938\text{ BeV}.

Water is flowing through a horizontal pipe line of varying cross-section. If the pressure of water equals 2\text{cm} of mercury at a point where velocity of the flow is 32\text{ cm/sec}. What is the pressure at another point where velocity of flow is 40\text{ cm/sec}?

A vessel of mass 10^7\text{ kg} is gyrostabilised by a uniform circular disc of mass 5\times 10^4\text{ kg} and radius 2\text{m} which rotates at 15\text{ rev/sec}. What is the angular momentum of the stabilizer ?

What is understood by the term ‘Coriolis force’? Obtain expressions for velocity and acceleration of a particle in rotating coordinate systems.

Write a shout note (about 200 words) on super-conductors and the nature of revolution that may come up if superconductors with critical temperature well above the room temperatures are developed.

Define Fermi energy. Show that the Fermi level lays half-way between the top of the valence band and the bottom of the conduction band of an intrinsic semiconductor. Explain why an extrinsic semiconductor, such as an N-type crystal, has more free electrons than holes but is found to be electrically uncharged.

Draw the circuit diagrams suitable for measuring the voltage amplification of a triode valve with the following methods of connection: (a) Common cathode (b) Common grid (c) Common anode. Write down, without proofs, the expression for amplification in each case in terms of \mu and the relevant resistance values. Which of the three methods is usually employed in high frequency circuit practices and why ?

Interpret the nuclear process described by the equation {}_{92}U^{235} + _{0}n^{1} \rightarrow _{92}n^{236} \rightarrow _{56}Ba^{141} + _{36}Kr^{92} + 3 _{0}n^{1} + Q The products of this kind of reaction vary widely, but the average Q is found to be 180 MeV. Compute the consumption rate of U^{235} per year if power generation is to be an average 100 MW. (Take efficiency = 1).

Write a brief note (about 200 words) on parity violation

Schematically draw the binding energy cone for atomic nuclei defining the parameters used. Explain how it indicates release of energy on fission of some nuclei and on fusion of other. Could one of these processes be the origin of solar energy?

Some amount of a radioactive substance (half-life=30\text{ days}) spread inside a room and consequently the level of radiation becomes 50 times the permissible level for normal occupancy of the room. After how many days the room would be safe for occupation?

The series limit due Balmer series for hydrogen is given by 3.65 \times 10^{-5}\text{ cm.} and an element is found to give k-series wavelength down to 10 \times 10^{-10}\text{ cm,} Find the atomic number of the element.

In observing the Raman spectrum of a sample, using 2537\text{ \AA} as the exciting line, one gets a Stokes line at 2683\text{ \AA}. Deduce the Raman shift in \text{cm}^{-1} units. What information does it give? Compute the wavelength, in \text{\AA} units, for the corresponding Stokes and anti-Stokes tines if the exciting line is 5461\text{ \AA}.

Define Compton wavelength for an electron. Calculate in electron-volts the photon energy corresponding to radiations of the Compton wavelength. What light does the Compton effect throw on the nature of X-rays?

Compare the energy of a photon with that of a neutron when both are associated with wavelength of 1\text{\AA}.