A uniform solid sphere of mass \(M\) and radius \(R\) is placed on a smooth horizontal surface. It is struck by a horizontal cue at a height \(h\) above the center. For the sphere to roll without slipping immediately after the impact, the value of \(h\) must be:
Show Hint
For a rigid body struck impulsively and required to roll immediately:
\[
Jh=I\omega
\]
along with
\[
v=\omega R
\]
For a solid sphere:
\[
I=\frac{2}{5}MR^2
\]
Always remember the standard result:
\[
h=\frac{2R}{5}
\]
above the center.