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Pure Rolling

A solid spher...

Question

A solid sphere of mass $M$ and radius $R$ is placed on a rough horizontal surface. It is stuck by a horizontal cuestick at a height $h$ above the surface. The value of $h$ so that the sphere performs pure rolling motion immediately after it has been struck is

A

\frac{2 R}{5}

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B

\frac{5 R}{2}

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C

\frac{7 R}{5}

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D

\frac{9 R}{5}

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Solution

The correct option is B $\frac{7 R}{5}$
About point O, Angular impulse, $H = J x$
$I w = (m v) x$
$\frac{2}{5} m R^{2} w = (m R w) x$ $v = R w$
$⟹ x = \frac{2}{5} R$
$h = x + R = \frac{7 R}{5}$

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