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JEE MainPhysicsLaws of Motion

A small block is placed against the inner vertical wall of a hollow cylinder of radius R . The cylinder is rotating about its vertical axis. If the coefficient of static friction between the block and the wall is , what is the minimum angular speed of the cylinder required to prevent the block from sliding down?

Options

  1. Ag R
  2. Bg R
  3. Cg R
  4. Dg R

Correct answer

B. g R

Step-by-step solution

Let the mass of the block be m . The normal force N exerted by the wall of the cylinder provides the necessary centripetal force for the block's circular motion: N = m ^2 R The block is prevented from sliding down by the static friction force f_s acting upwards. For vertical equilibrium, this friction must balance the gravitational force: f_s = mg The condition for the block not to slide is that the required static friction must not exceed the maximum limiting friction: f_s N Substituting the expressions for f_s an

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