A large drum having radius R is spinning around its axis with angular velocity , as shown in figure. The minimum value of so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M as , is :

Step-by-step solution

Consider the mass M in the frame of the rotating drum. The forces acting on the mass are: 1. Weight Mg acting vertically downwards. 2. Normal reaction N from the wall acting towards the center, which provides the centripetal force: N = M ^2 R . 3. Frictional force f acting vertically upwards to balance the weight. For the mass to remain stuck to the wall, the frictional force must balance the weight: f = Mg . The maximum available static friction is f_ max = N = M ^2 R . To prevent slipping, we must have f_ max Mg