Question

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be (g = 10 m/s²)
(1) (√10) rad/s
(2) (10/2π) rad/s
(3) 10 rad/s
(4) 10π rad/s

Answer 1

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Answer 2

The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be 10 rad/s.

Step by step explanation:

From the diagram,

                   $f_{L}\geq mg$

               $\Rightarrow \mu N\geq mg$

              $\Rightarrow \mu mr\omega ^{2}\geq mg$

cancel the same constants on the both sides.

               $\Rightarrow \mu r\omega ^{2}\geq g$

               $\Rightarrow \omega \geq \sqrt{\frac{g}{r\mu }}$

              $\Rightarrow \omega_{min} = \sqrt{\frac{g}{r\mu }}$.......................(1)

From the given,

Mass of block = 10 kg

Radius of cylindrical drum = 1 m

Substitute the given values in equation (1)

               $\Rightarrow \omega_{min} = \sqrt{\frac{10}{0.1\times 1}}=10\,rad/s$

Therefore, the angular velocity of cylinder is 10 Rad/s

Hence, correct answer is 3