A coin is placed on a disc rotating with an angular velocity . The co-efficient of friction between the disc and the coin is . The maximum distance of the coin from the centre of the disc up to which it will rotate with the disc is

Step-by-step solution

For the coin to rotate with the disc without slipping, the centripetal force required for circular motion must be provided by the static frictional force. Let m be the mass of the coin, r be the distance from the centre, and be the angular velocity. The centripetal force is F_c = m ^2 r . The maximum static frictional force available is f_ max = N , where N = mg is the normal force. Thus, f_ max = mg . For the coin to remain stationary relative to the disc, the condition is F_c f_ max . m ^2 r mg . Solving for the