A large drum having radius R is spinning around its axis with angular velocity ω, as shown in figure. The minimum value of ω 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 is μ, is :

Question

G1 Physics · Accepted Answer

The normal reaction from the wall provides the centripetal force: N = Mω²R. The block tends to slide downward because of gravity. For the limiting condition of no downward slipping, the maximum static friction balances the weight: μN = Mg. Substitute N = Mω²R: μMω²R = Mg. Cancel M: μω²R = g. Therefore, ω² = g/(μR), and ω(min) = √[g/(μR)]. Correct option: D.