A uniform solid. cylinder `A` of mass can freely rotate about a horizontal axis fixed to a mount of mass `m_(2)`. A constant horizontal force `F` is applied to the end `K` of a light thread tightly wound on the cylinder. The friction between the mount and the supporting horizontal plane is assumed to be absent. Find the acceleration of the point `K`.

Explanation

The acceleration whole system `a_(1)=F/(m_(1)+m_(2))`
The acceleration of the point `K` w.r.t the axis of the cylinder `a_(2)=alphaR`
where `alpha` is given by
`FR=Ialpha` or `alpha=(FR)/(m_(1)R^(2)//2)=(2F)/(m_(1)R)`
`implies a_(2)=(2F)/m_(1)`
The acceleration of the point `K` w.r.t ground
`=a_(1)+a_(2)=F/(m_(1)+m_(2))+(2F)/m_(1)=F((3m_(1)+2m_(2)))/(m_(1)(m_(1)+m_(2)))`