A large drum having radius 
is spinning around its axis with angular velocity 
, as shown in figure. The minimum value of 
so that a body of mass 
remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass 
as 
, is:
Text Solution
Verified by ExpertsD
Consider the mass 
in the frame of the rotating drum. The forces acting on the mass are:
(i) Weight 
acting vertically downwards.
(ii) Normal reaction 
from the wall acting towards the center, which provides the centripetal force: 
.
(iii) Frictional force 
acting vertically upwards to balance the weight.
For the mass to remain stuck to the wall, the frictional force must balance the weight: 
.
The maximum available static friction is 
.
To prevent slipping, we must have 
.
The minimum value of 
is 
.
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