First slide

Rolling motion

Question

Figure shows a hemisphere of radius 4R. A ball of radius R is released from position P. It rolls without slipping along the inner surface of the hemisphere. Linear speed of its centre of mass when the ball is at position Q, is:

Easy

A

$\sqrt{\frac{30 gR}{7}}$
B

$\sqrt{\frac{24 gR}{5}}$
C

$\sqrt{\frac{40 gR}{9}}$
D

$\sqrt{6 gR}$

Solution

From COME, $mg (4 R - R) = \frac{1}{2} {mv}^{2} (1 + \frac{2}{5})$
$\Rightarrow 3 mgR = \frac{7}{10} {mv}^{2} \Rightarrow v = \sqrt{\frac{30 gR}{7}}$

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