A couple produces a:

A cylindrical solid of mass M has raidus R and length L. Its moment of inertia about a generator is:

A man of mass M is standing at the centre of a rotating turn table rotating with an angular velocity w. The man holds two 'dumb bells' of mass M/4 each in each of his two hands. If he stretches his arms to a horizontal position, the turn table acquires a new angular velocity w' where

A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is

A loaded spring gun of mass M fires a 'shot' of mass m with a velocity \(\vartheta \) at an angle of elevation \(\theta\). The gun is initially at rest on a horizontal frictionless surface. After firing, the centre of mass of the gun-shot system

A ball is moving with a velocity of 10m/s. Suddenly, it breaks into two equal parts. What will be the speed of centre of mass of the system after explosion?

A ballet dancer stretches her hand out for slowing down. Name the conservation obeyed.

If a cube is melted and is casted into a sphere, does moment of inertia about an axis through centre of mass increase or decrease.

A faulty balance with unequal arms has its beam horizontal. Area the weights of the two pans equal?

Find the centre of mass of a triangular lamina.

A person is standing on a rotating table with metal spheres in his hands. If he withdraw his hands to his chest, what will be the effect on his angular velocity?

Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius about an axis passing through their axis of symmetry?

Two boys of the same weight it at the opposite ends of a diameter of a rotating circular table. What happens to the speed of rotation if they move nearer to the axis of rotation?

If ice on poles melts, then what is the change in duration of day?

The speed of the whirl wind in a tornado is alarmingly high. Why?

Does tile radius of gyration depend on the angular velocity of the body?

If a string of a rotating stone breaks, in which direction will the stone move?

Which component of a force does not contribute towards torque

Two satellites of equal masses are orbiting at different heights. Will their moments of inertia be the same or different?

What is moment of inertia of a solid sphere about its diameter?

Three identical spheres each of radius r and mass m are placed touching each other on a horizontal floor. Locate the position of centre of mass of the system.

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

Fig. shows two blocks of masses 5kg and 2kg placed on a frictionless surface and connected by a spring. An external kick gives a velocity 14 m/s to the heavier block in the direction of lighter one. Deduce (a) the velocity gained by the centre of mass and (b) the separate velocities of the two blocks in the centre of mass coordinates just after the kick.

lf earth contracts to half its radius, what would be the duration of the day?

Angular momentum of a system is conserved if its M.I. is changed. ls its rotational K.E. also conserved?

Two bodies of masses 1 kg and 2 kg are located at (1, 2) and (-1, 3), respectively. Calculate the coordinates of the centre of mass.

In given pulley mass system, mass m₁ = 500 g, m₂ = 460 g and the pulley has a radius of 5 cm. When released from rest, heavier mass falls through 7.50 cm in 5 s. There is no slippage between pulley and string.
(i) What is magnitude of acceleration of mass?
(ii) What is magnitude of pulley's angular acceleration?

Discuss the rolling motion of a cylinder on an inclined plane.

Locate the centre of mass of a system of particles of mass m₁ = 1 kg, m₂ = 2 kg and m₃ = 3 kg, situated at the corners of an equilateral triangle of side 1.0 metre.