A solid sphere (A) of mass $$5m$$ and a spherical shell (B) of mass $$m$$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of $$a_A$$ and $$a_B$$, respectively. The ratio of $$a_A$$ and $$a_B$$ is __________.

$$a_A = \frac{2F}{M_A + \frac{I_A}{R^2}}$$

$$a_A = \frac{2F}{5m + \frac{2mR^2}{R^2}} = \frac{2F}{5m + 2m} = \frac{2F}{7m}$$

$$a_B = \frac{2F}{M_B + \frac{I_B}{R^2}}$$

$$a_B = \frac{2F}{m + \frac{\frac{2}{3}mR^2}{R^2}} = \frac{2F}{m + \frac{2}{3}m} = \frac{2F}{\frac{5}{3}m} = \frac{6F}{5m}$$

$$\frac{a_A}{a_B} = \frac{\frac{2F}{7m}}{\frac{6F}{5m}} = \frac{2}{7} \times \frac{5}{6} = \frac{10}{42} = \frac{5}{21}$$