UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Find the power dissipated by R and power stored in L.

At what time are these voltage drops equal?

Calculate the voltage drops across R and across L.

What is the limiting case of a metallic conductor in the above case ? Explain

When fixed at both ends, a wire under tension of 900\text{ N} and having a linear density 10^{-2}\text{ kg/m} is resonant at the frequency of 420\text{ Hz}. The next higher frequency at which it resonates is 490\text{ Hz}. What is the length of the wire.

Four perfect polarizing plates are stacked so that the axis of each is turned 30 clockwise with respect to the preceding plate: the last plate is crossed with the first. How much of the intensity of an incident unpolarized light is transmitted by the stack ?

How does the resolving power of a microscope differ from that of a telescope ? Find the resolving power of an electron microscope that uses 15\text{ Key} electrons, assuming that this is equal to the electron wavelength.

Explain in detail how one can obtain fringes with the Michelson Interferometer using incandescent lamps.

A book sits on a horizontal board that is undergoing simple harmonic motion with amplitude of 1\text{ m}. The coefficient of friction between the book and the board is \mu = 0.5. Find the frequency of the motion of the board at which the book is about to slip.

Show that Simple Harmonic Motion can he described as the projection on its diameter of a uniform circular motion.

The case of a Simple Harmonic Progressive Wave traversing through a medium is expressed as y = 4 \times 10^{-5} \sin(600\ \pi t + \varphi) Determine

(i) amplitude of vibration of the particles.

(ii) wavelength of the sound wave and

(iii) the phase difference between the particles situated at a distance of 22\text{ cm}. (The sound velocity in the medium is 3.4 \times 10^4\text{ cm/s}).

The maximum pressure variation P that the human ear can tolerate in loud sounds is about 28\text{ nt/m}^2. Normal atmospheric pressure is about 100,000\text{ nt/m}^2. Find the corresponding maximum displacement for a soundwave in air having a frequency of 100\text{ cycles/second}. (Take velocity of sound in air as 331\text{ m/sec.} arid density of air = 1.22\text{ kg/m}^3)

Write a short note on Holography.

What is 'Loren & Contraction' ? A spaceship of rest length 100\text{ mm} takes 4\ \mu\text{s} to pass an observer on Earth. What is its velocity relative to the Earth?

Using Bernoulli's principle indicate how to compute the thrust on a rocket produced by the escape of its exhaust gases.

A top is spinning about its axis of symmetry. If its spin angular momentum is large compared to the change caused by the applied torque the top processes. If it is not spinning, the top would tip over. Show what happens in between, when the top spins slowly. Derive an approximate expression for the angular speed of the precessional motion.

Write a short note on Coriolis force.

Ram and Shyam are two skaters weighing 40\text{kg} and 60\text{ kg} respectively. Ram travelling at 4\text{ m/s} meets Shyam travelling at 2\text{ m/s} in opposite direction and collides head-on.

(i) If they remain in contact what is their final velocity ?

(ii) How much kinetic energy is lost ?

Show that the combined effects of translation of the centre of mass and rotation about an axis through the centre of mass are equivalent to a pure rotation with the same angular speed about an axis through the point of contact of a rolling body.

The mass of the Moon is about 0.13 times the mass of the Earth. The distance from the centre of the Moon to the centre of the Earth is 60 times the radius of the Earth. Taking the Earths radius to be 6378\text{ km}. find out the distance of the centre of mass of the Earth - Moon system from the centre of the Earth.