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A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1m. 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 is axis, will be

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a

$\frac{10}{2 π} rad / s$

b

$10 πrad / s$

c

10 rad/s

d

$\sqrt{10} rad / s$

answer is A.

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Detailed Solution

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For equilibrium of the block limiting friction
$\begin{array}{l} f_{L} \geq mg \Rightarrow μN \geq mg \Rightarrow {μmrω}^{2} \geq mg \\ ω \geq \sqrt{\frac{g}{rμ}} \Rightarrow ω_{min} = \sqrt{\frac{g}{rμ}} \\ ω_{min} = \sqrt{\frac{10}{0.1 \times 1}} = 10 rad / s \end{array}$

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A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1m. 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 is axis, will be