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A rough platform OA rotates in a vertical plane about a horizontal axis through the point O with a constant counter clockwise velocity $ω = 3 rad s^{- 1}$ . As it passes through the point $θ = 0$ , a small mass m is placed at a radial distance $r = 0 .5 m$ . If the mass is observed to slip at $θ = 37^{0}$ , then the coefficient of friction between the mass & the member is

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$\frac{3}{16}$

$\frac{9}{16}$

$\frac{4}{9}$

$\frac{5}{9}$

answer is A.

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Detailed Solution

As the mass is at the verge of slipping
$\begin{array}{l} ∴ mgsin 37 - μmgcos 37 = {mω}^{2} r \\ 6 - 8 μ = 4 .5 \\ ∴ μ = \frac{3}{16} \end{array}$

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