UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Give a mathematical analysis of forced vibration and hence explain the phenomenon of amplitude resonance.

A diffraction grating with 3 \times 10^4 lines is used in the second order in the range of wavelength 6000\text{\AA}. Find the smallest \Delta\lambda it can resolve.

The half-life of \mu-meason at rest is 2 \times 10^{-8}\text{ sec}. Determine the half life of \mu-meason while travelling with half the speed of light in vacuum.

State Kepler's laws of planetary motion. Why does a missile need an escape velocity to escape from earth?

Calculate the speed of a satellite orbiting the planet Jupiter at a distance of 108\text{ km}, above its surface (The mass and radius of Jupiter are 1.9 \times 10^{27}\text{ kg} and 69892\text{ km} respectively.)

Write down the expression for the dependence of mass of a particle on its velocity in special relativity. What will be the speed of a particle if its mass becomes double of its rest mass ?

What do you mean by centre of mass of a system of particles? Derive expressions for the instantaneous position vector and velocity of the centre of mass of such a system of particles.

Using Rutherford's observation that the number of \alpha particles scattered at an angle \phi and falling on unit area of the screen varied as (\text{cosec }(\phi/2))^4, deduce an expression for the probability of scattering between angles \phi and \phi + d\phi.

State Bernoulli's theorem. Find out the velocity of efflux of a liquid from a reservoir in which the pressure is 3.5 \times 10^5\text{ N/m}^2 above the atmospheric pressure. The density of the liquid is 700\text{ kg/m}^3.

Write a short note on Inertial forces in a rotating frame.

Write a short note on Gyroscope and its application.

Write a short note on The Lorentz transformation.

Why do the electronic energy level in a solid form bands? Describe in terms of the band theory the difference between a conductor, an intrinsic semi-conductor and an insulator. How does the energy level change when some impurities are introduced in a semiconductor? Explain how by doping you have both n-type and p-type semiconductors starting with pure Germanium. The band gap in cases of Germanium is about 0.8\text{ eV} at Ok. Neglecting the variation of band gap with temperature, make a rough estimate of the temperature at which the resistance of a pure Germanium sample will be reduced to 1/e times its value at 300k.

A nuclear transition in a nucleus of mass 24 a.m.u. emits a gamma photon of energy E_1 if the transition occurs when the nucleus was bound in a crystal, and of energy E_1 if the transition occurs when the nucleus were free. Deduce the difference [E_1 - E_2] in keV units if E is in the range 7 meV.

Give, in short the principle of working of mass spectrograph (any type). What does it determine? What are isotopes? How many isotopes of hydrogen do you know of? Are they all stable? The minimum energy required for the disintegration of the nucleus of a stable isotope of hydrogen is 2.21\text{ MeV}. Calculate the mass of this nucleus in a.m.u.

Explain why Light elements like hydrogen and deuterium are effective in shielding against neutrons while heavy elements like lead are effective in case of gamma rays.

Give the quantum numbers of the states whose energy difference accounts for the two D-lines of sodium. Find the energy difference for D_1 and D_2 lines in electron volts. (Wavelength separation = 6\text{\AA}, Mean wavelength = 5893\text{\AA})

How do characteristic X-ray lines originate? Using Bohr's atomic model deduces a relation between the frequencies of the K series X-ray lines and atomic numbers of the emitting elements. Do you expect this relation to be exact?

What is the value of the spin of the electron and the corresponding magnetic-moment? Can that be considered as arising from the classical case of rotation of a finite rigid charged body about its axis? Give reasons for your answer.

What are de Broglie waves? State the uncertainty principle and explain its relation with de Broglie waves by considering a free particle.