System of Parti...

Can centre of mass of a body coincide with the geometrical centre of the body?

For a given mass and size, moment of inertia of a solid disc is smaller than that of a ring. Why?

A one kg ball rolling on a smooth horizontal surface at 20 \(ms^{-1}\) comes to the bottom of an inclined plane making an angle of 30° with the horizontal. Calculate K.E. of the ball when it is at the bottom of incline. How far up the incline will the ball roll? Neglect friction.

A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of \(\frac{3v^2}{4g}\) with respect to the initial position. Name the given object.

Where does the centre of mass of a uniform triangular lamina lie?

Isolated system is...............

For which of the following does the centre of mass lie outside the body?

When a disc rotates with uniform angular velocity, which of the following is not true?

A Merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed \(\omega\). A person of mass M is standing on it. At one instant, the person jumps off the round, radically away from the centre of the round (as seen from the round). The speed of the round afterward is

Choose the correct alternatives:

The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?

Identify the correct statement for the rotational motion of a rigid body

A solid sphere is rolling on a frictionless plane surface about its axis of symmetry. Find ratio of its rotational energy to its total energy.

A solid sphere is rotating about a diameter at an angular velocity \(\omega\). If it cools so that its radius reduces to 1/n of its original value, its angular
velocity becomes \(\frac{\omega}{n^2}\)

If the original rotational K.E. of the sphere is K, Its new value will be............

If radius of solid sphere is doubled by keeping its mass constant, then

M.I. of a thin uniform circular ring about the tangent to the plane of the ring is

Ratio of rotational K.E. to linear K.E. of a solid sphere is

A dancer on ice spins faster when she folds here arms. This is due to

A particle of mass m is moving with a constant velocity along a line parallel to the +ve direction of the X-axis. The magnitude of its angular momentum w.r.t the origin on z- axis