A coin is placed on a disc. The coefficient of friction between the coin and the disc is μ . If the distance of the coin from the center of the disc is r , the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

Step-by-step solution

Normal force acting on the coin is, N = m g . Required friction force to provide centripetal force for the coin is, f = m ω 2 r and maximum value of static friction force available is, f = μ N = μ m g . For limiting condition, we can write ⇒ μ m g = m r ω 2 ⇒ ω = μ g r