A force F acts tangentially at the highest point of a sphere of mass m kept on a rough horiozontal plane. If the sphere rolls withut slipping, find the accelerastioni of the centre of the sphere.

Explanation

The situation ikn shown in ure. As the force F rotates the sphere , the point of contact has a tendency to slip twoards left sothat the static friction on the shre will act towards rith. Let r be the radius of hte sphere aN/A be the linear accelerastion about the centre of the sphere is `alpha=a/r` as there is no centre
`F+f=ma`...........i
`and the rotatioN/Al motin about the centre
`Fr-fr=Ialpha=2/5 mr^2)(a/r)`
`or F-f=2/5ma`.......ii
`from i and ii
`2F=7/5maor, a=(10F)/(7m)`.