Question 133 of 210
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 :
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Answer: (D)
Consider the mass in the frame of the rotating drum. The forces acting on the mass are:
1. Weight acting vertically downwards.
2. Normal reaction from the wall acting towards the center, which provides the centripetal force: .
3. 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 .
1. Weight acting vertically downwards.
2. Normal reaction from the wall acting towards the center, which provides the centripetal force: .
3. 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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