Question

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?

Answer 1

`F-f=Ma` ..(i)
`tau=Ialpha=I((alpha)/(R))`
`impliesf.R=(2)/(5)MR^(2)(a)/(R)`
`impliesf=(2)/(5)Ma`

Solving Eqs. (i) and (ii) we get
`f=(2)/(7)F`
`(2)/(7)Flemumg`
`impliesFle(7)/(2)mumg`