A horizontal force `F` acts on the sphere at its centre as shown. Coefficient of friction between ground and sphere is `mu`. What is maximum value of `F` for which there is no slipping?

Explanation

For linear motion `F - f = Ma`
and for rotational motion `tau - I alpha`
`rArr f.R = (2)/(5)MR^(2).(a)/(R ) rArr f=(2)/(5)Ma` or `Ma=(5)/(2)f`
`therefore F-f=(5)/(2)f` or `f=(2F)/(7)`
`therefore f le Mg therefore (2F)/(7) le mu Mg` so `F le (7)/(2) mu Mg`.