Solve the following :


A thin spherical shell lying on a rough horizontal surface is hit by cue in such a way that the line of action passes through the centre of the shell. As a result the shell starts moving with the linear speed v without any initial angular velocity. Find the linear speed of the shell after it starts pure rolling on the surface.


By angular momentum conservation at bottom most point


$m v R=m v^{\prime} R+I \omega^{\prime}$

$m v R=\left(\frac{2}{3} m R^{2}\right)\left(\frac{v^{\prime}}{R}\right)+m v^{\prime} R$

$v^{\prime}=\frac{3 v}{5}$

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