A tangential force acting on the top of sphere of mass m kept on a...

Let $a$ be the acceleration of centre of sphere. The angular acceleration about the centre of the sphere is $\alpha=\frac{a}{r}$, as there is no slipping. For the linear motion of the centre $f+F=m a$ ...(i) and for the rotational motion about the centre $F r-f r=I \alpha=\left(\frac{2}{5} m r^2\right)\left(\frac{a}{r}\right)$\Rightarrow \quad F-f=\frac{2}{5} m a$...(ii) From Eqs. (i) and (ii)$2 F=\frac{7}{5} m a \Rightarrow a=\frac{10 F}{7 m}