Question

A solid sphere is kept on a rough horizontal surface. A horizontal force ${}^{\prime }{F}^{\prime }$ is applied at centre. Calculate the acceleration of the sphere.

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

Answer 1

The correct option is A $\frac{5F}{7m}$

Applying Newtons second law,
$\begin{array}{cc}\tau =I\omega & F-f=ma\\ f.R=\frac{2}{5}M{R}^2\times \frac{a}{R}& F-\frac{2}{5}ma=ma\\ f=\frac{2}{5}ma& a=\frac{5F}{7m}\end{array}$