A tangential force `F` acts at the top of a thin spherical shell of mass `m` and radius `R`. Find the acceleration of the shell if it rolls without slipping.

Explanation

Let `f` be the force of friction between the shell and the horizontal surface

For translational motion
`F + f = ma` ….(i)
For rotational motion,
`FR-fR=Ialpha=I(a)/(R) (because a =R alpha "for pure rolling")`
`rArr F-f=I(a)/(R^(2))`...(ii)
Adding Eqs. (i) and (ii)
`2F=(m+(I)/(R^(2)))a=(m+(2)/(3)m)a=(5)/(3)ma`
or `F=(5)/(6)ma" "[because I_("shell")=(2)/(3)mR^(2)]`
`rArr a=(6F)/(5m)`.