Define couple.

State principle of moments

Define centre of gravity.

Mention any two physical significance of moment of inertia?

What is radius of gyration?

State conservation of angular momentum. 

What is rolling motion?

The diameter of a solid disc is 0.5m and its mass is 16kg. What torque will increase Its angular velocity from zero to 120 rotations/minute in 8 seconds?

Write the equation for the CM of two point masses when,
(i) Masses are on positive x-axis
(ii) Origin coincides with anyone of the masses 
(iii) origin coincides with CM itself.

Explain Right hand rule to find the direction of Torque.

The maximum and minimum distances of a come from the sun are 1.4\(\times\)10¹²m and 7\(\times\)10¹⁰m. If its velocity nearest to the sun is 6 \(\times\) 104 ms^-1, what is the velocity in the farthest position? Assume that path of the comet in both the instantaneous positions is circular.

Three mass points m₁ m₂ and m₃ are located at the vertices of an equilateral triangle of length a. what is the moment of inertia of the system about an axis along the altitude of the triangle passing through m₁?

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is angular acceleration of the cylinder if the rope is pulled with a force of 30N? What is the linear acceleration of the rope? Assume that there is no slipping.

Give the physical significance of moment of inertia. Explain the need of fly wheel in Engine.

Three masses 3 kg, 4 kg and 5 kg are located at the corners of an equilateral triangle of side 1 m. Locate the center of mass of the system.

Calculate the ratio of radius of gyration of a circular ring and a disc of the same radius with respect to the axis passing through their centres and perpendicular to their planes.

A child stands at the centre of turn table with his two arms out stretched.
(i) The turn table is set rotating with an angular speed of 40 rpm. How mueh is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/3 times the initial value? Assume that the turn table rotates without friction.
(ii) Show that the child's new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy ?

Find the moment of inertia of a uniform rod about an axis which is perpendicular to the rod and touches anyone end of the rod.

A rolling wheel has velocity of its center of mass as 5 ms^-1. If its radius is 1.5 m and angular velocity is 3 rad s^-1 then check whether it is in pure rolling or not.

Consider a thin uniform circular ring rolling down in an inclined plane without slipping. Compute the linear acceleration along the inclined plane if the angle of inclination is \(45 ^{0}\).

State Newton’s Universal law of gravitation.

Will the angular momentum of a planet be conserved? Justify your answer.

Define the gravitational field. Give its unit.

Define gravitational potential energy.

Is potential energy the property of a single object? Justify.

Define gravitational potential.

What is the difference between gravitational potential and gravitational potential energy?

Why is the energy of a satellite (or any other planet) negative?

Define weight.

Why is there no lunar eclipse and solar eclipse every month?