A sphere of mass m and radius R is kept on a rough wedge. The acceleration of wedge for the sphere to remain in equilibrium with respect to wedge should be.3

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$\frac{g}{\sqrt{3}}$

$g \sqrt{\frac{2}{3}}$

$g \frac{\sqrt{2}}{3}$

$g \sqrt{\frac{3}{2}}$

answer is C.

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Detailed Solution

$\begin{array}{l} τ_{contactpoint} = 0 \\ \Rightarrow τ_{mg} = τ_{ma} \\ \Rightarrow Rmgsin 30^{\circ} = R ma \cos 30^{\circ} \\ \Rightarrow a = \frac{g}{\sqrt{3}} \end{array}$

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