In the figure shown, a force F is applied at the top of a disc of mass 4 kg and radius 0.25 m. find maximum velue of F for no slipping.

Explanation

Till pure rolling continues we can fin `alpha` about bottommost point. About bottommost point torque of friction is zero.
`alpha=(F(2R))/(3//2)mR^(2)=(4F)/(3mR)`
`a=Ralpha=(4F)/(3m)`
`F+f_(max)=ma=(4F)/(3)`
`F=3f_(max)=ma=(4F)/(3)`
`F=3f_(max)=3mumg`
`=3xx0.6xx4xx10=72N`
This is the maximum value of applied force, as we have taken the maximum friction.