What will be the velocity of rotation of earth about its own axis so that a body becomes weightless at the equator?

What will be the velocity of rotating of earth about its own axis so that a body becomes weightless at the equator ?

Calculate the angular velocity of earth about its own axis.

What is the kinetic energy of a rotating body about its axis of rotation ?

What will be the angular velocity of the diurnal motion of the earth, so that the weight of a body at the equatorial region is 0.6 of the present weight? Radius of the earth = 6400 km.

Statement I : Many great rivers flow towards the equator. The sediments that that they carry increase the time of rotation of the earth about its own axis. Statement II : The angular momentum of the earth about its rotation axis is conserved.

What is the value of escape velocity of earth?

A hollow cylinder of radius r is rotating about its own vertical axis. Both ends of the cylinder are open. A piece of stone of mass m remains fixed on the inner side of the cylinder. What should be the minimum velocity of rotation of the cylinder so that the stone remains fixed on the surface of the cylinder without falling down? Coefficient of static friction between the wall of the cylinder and the stone = mu , acceleration due to gravity = g. Also, prove that this velocity is independent of the mass of the stone.