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A block of mass 20 kg is in contact against the inner wall of a hollow cylindrical drum of radius 2 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.2 . 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 $(g = 10 m / s^{2})$

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$5 π rad / s$

$\sqrt{5} rad / s$

$\frac{5}{2 π} rad / s$

$5 rad / s$

answer is D.

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Detailed Solution

$To keep the block stationary, Frictional force \geq Weight μN \geq Mg Here, N = {Mω}^{2} r r = 2 m, μ = 0.2 For minimum ω, \Rightarrow {μMω}^{2} r = Mg \Rightarrow ω = \sqrt{\frac{g}{μr}} = \sqrt{\frac{10}{0.2 \times 2}} = 5 {rads}^{- 1}$

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