UPSC Physics Optional PYQs (CSE & IFoS)PYQs

The potential energy of a particle is given by U = a \cos \alpha x Obtain the positions of stable equilibrium.

The distance between the centres of oxygen and carbon atoms in a carbon monoxide molecule is 1.2\text{ \AA}. Determine the position of the centre of mass of the molecule relative to carbon. (Assume atomic masses of carbon and oxygen as 12 and 16 respectively.)

State and explain variation mass with velocity, hence find an expression for the density of a body in an arbitrary inertial frame of reference.

Explain what you mean by processional torque. Deduce an expression for the time period of processional motion of gyroscope in terms of relevant quantities.

If the earth were to rotate at n times its present speed of rotation about its axis, the apparent weight of a body at the equator would assume zero value. Find an expression for n.

Explain what is meant by Coriolis force. Discuss the action of Coriolis force on a body failing freely on the earth at altitude \lambda.

What is centre of mass? Show that there exists only one centre of mass in system of particles. Discuss the usefulness of centre of mass in studying motion of system of particles.

Write a short note on Geostationary satellite.

Write a short note on Rutherford scattering.

Write a short note on Lorentz transformation.

Find the fractional decrease of kinetic energy of a particle of mass m_1 when a head-on elastic collision takes place with another particle of mass m_2 initially at rest. In this context show why hydrogen would be best to be used for slowing down neutrons. Actually \text{D}_2\text{O}, not \text{H}_2\text{O} is used why?

A rocket of mass 1000\text{ kg} is ready for a vertical take off. The exhaust velocity of its fuel is 4.5\text{ km/s}. Deduce (i) the minimum rate of fuel ejection so that the rocket weight be just balance, (ii) the velocity acquired in 8\text{ s} if the fuel ejection rate is 2.50\text{ kg/s}. (You may neglect the effect of changing mass of the rocket in the given conditions.)

Write a short note on Mass energy equivalence.

State Lorentz transformation equations. Show that for v/c \ll 1, the lorentz transformation equations reduce to Galilean transformation equations. Explain the physical significances of Larentz transformations.

Write a short note on Conchs forces.

A radioactive nucleus mass m_0\text{ amu} emits an alpha particle with kinetic energy E_a. If the disintegration occurs when the nucleus is free, deduce an expression for the energy evolved (E_t) during the disintegration.

Define Reynold's number, the cross sectional radius of a pipeline decreases following the relation. r = r_0 e^{-ax}, where a = 0.6\text{ m}^{-1}, x is the distance (in \text{m}) from the pipeline inlet. Calculate the ratio of Reynold's number for two cross sections separated by \Delta x = 3\text{m}.

A top is spinning with an angular velocity \omega about its axis which is initially vertical Find the condition of stability, if the axis be given a slight nutation.

Prove that the rate of angular momentum of a system about a fixed line is equal to the total torque of the external forces about that line

A satellite, revolving in a circular equatorial orbit at height 1.36 \times 10^4\text{ km} from earth's surface from west to east, appears over some spot at the equator every 6\text{ hrs}. Show that the data are consistent with known earth's radius 6.4 \times 10^3\text{ km} and g = 9.8\text{ ms}^{-2} at earth's surface.