# A thin spherical shell lying on a rough horizontal surface is hit by a 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 a linear speed V with out any initial angular velocity. Find the speed of the shell after it starts pure rolling on the surface .

$\begin {array} {1 1} (a)\;\frac{3v}{5} & \quad (b)\;\frac{3v}{2} \\ (c)\;\frac{v}{2} & \quad (d)\;\frac{v}{5} \end {array}$

Applying angular momentum conservation about the bottom most point.
$MVR= MV'R+Iw$$\qquad [w= \large\frac{V'}{R}] MVR= MV'R+\large\frac{2}{3}$$MR^2 \large\frac{V'}{R}$
$MVR=\large\frac{5}{3}$$MV'R V'=\large\frac{3}{5}$$V$
edited Jun 24, 2014