Gem stones such as ruby and emerald own emerald owe their color to

How the gem stones ruby exhibits red colour and emerald exhibits green colour ?

Precious stones, such as gem stones, are products of

Precious stones, such as gem stones, are products of

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.