Physics - Rotation Question with Solution | TestHub

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 $f+F=ma$ ...(i) and for the rotational motion about the centre $Fr-fr=I\alpha =\left(\frac{2}{5}m{r}^2\right)\left(\frac{a}{r}\right)$ $\Rightarrow F-f=\frac{2}{5}ma$ ...(ii) From Eqs. (i) and (ii) $2F=\frac{7}{5}ma\Rightarrow a=\frac{10F}{7m}$