PYQ Bank

Obtain the equation of motion of a particle moving relative to a rotating frame of reference. Explain the term representing coriolis force in this expression.

A person in a spaceship is holding a rod of length of 0.5 m, the space ship is cruising at a speed V parallel to the earths surface. What does the person in the space ship notice as the rod is rotated from parallel to perpendicular to the space ships motion? What does an observer on earth's surface notice?

The mass of muon at rest is 207\text{ m}_e where m_e is the electron rest mass (0.511\text{ MeV}). The mean life time at rest for muon is 2.2\ \mu\text{s}. The life time of muon emerging from an accelerator is measured in the laboratory as 6.9\ \mu\text{s}. Estimate the speed of these muons in the laboratory.

Define scattering cross-section. A charged particle of mass m and charge Z_e is scattered by another charged particle of charge Z_e at rest. Deduce the expression for the scattering cross-section.

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

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?

Write a short note on Coriolis force.

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.

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 ?

An aeroplane makes a complete half circle of 50\text{ m} radius towards left when flying at 200\text{ km / hour}. The rotary engine and the propeller of the plane weigh 400\text{ kg} having a radius of gyration of 30\text{ cm}. The engine rotates at 2400\text{ rpm} clockwise viewing from the rear. Find the gyroscopic couple on the aircraft.

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.

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.

Neptune's period of revolution is 165\text{ yr}. What is the average radius of Neptune's orbit in teams of the Sun-Earth distance?

Derive an expression for the mass-energy equivalence using the principle of special relativity.

Explain the precession of a spinning top and show that precssional angular velocity is independent of the angle of inclination. A top is spinning with 20 rev/s about an axis inclined at 30^\circ with the vertical. Its radius of gyration is 5 cm. The centre of mass is \pi cm from the pivot point. Calculate the frequency of precession.

Write a short note on Applications of Bernoulli's equation.

Discuss the Reynolds number for describing the stability of fluid flow, Air streams horizontally across an aeroplane wing of area 4\text{ m}^2 and weighing 300 kg. The air speed is 60 m/s and 40 m/s over the top surface and under the bottom surface respectively. Find (i) the lift on the wing and (ii) the net force on it, given that the density of air is equal to 1.293\text{ kg/m}^3.

Starting from the definition of angular momentum of a single particle, obtain an expression for the angular momentum of a rotating rigid body. Hence, discuss the time derivative of the angular momentum and deduce the law of conservation of momentum.

Consider the motion of a rocket in a gravitational field and derive an expression for its final velocity when the fuel burns at a constant rate till it is fully consumed.

Describe the set-up of Michelson-Morley experiment. Why was a fringe shift expected in it? How are its negative results understood?