Question

A tangential force $F$ acts at the top of a thin spherical shell of mass $m$ and radius $R$ . The acceleration of the shell, if it rolls without slipping is

• A. $\frac{5 F}{6 m}$
• B. $\frac{6 F}{5 m}$
• C. $\frac{7 m}{2 F}$
• D. $\frac{2 m}{7 F}$

Answer 1

Answer: (B)

torque about 'O' $\tau = I \alpha $
$F \left(\right. 2 R \left.\right) = \alpha \frac{5}{3} m R^{2}$
$\alpha = \frac{6 F}{5 m R}$
Linear acceleration $a = R \alpha = \frac{6 F}{5 m}$