Solve the following :


A thin spherical shell of radius $R$ lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?


$v_{C}=R \omega$ (Pure Rolling)

By angular momentum conservation

$m v_{C} h=I \omega$

$m v_{C} h=\left(\frac{2}{3} m R^{2}\right)\left(\frac{v}{R}\right)$

$h=\frac{2 R}{3}$

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