Question

A tangential force $10\text{N}$ acts at the top of a thin spherical shell of mass $2\text{kg}$. Find the acceleration of the shell if it rolls without slipping.

• A. $3{\text{m/s}}^2$
• B. $4{\text{m/s}}^2$
• C. $6{\text{m/s}}^2$
• D. $8{\text{m/s}}^2$

Answer 1

The correct option is C $6{\text{m/s}}^2$

Let $f$ be the force of friction between the shell and the horizontal surface, $a$ is linear acceleration, and $\alpha$ is angular acceleration of the spherical shell.


For translation motion,
$10+f=ma=2a$ ............ (1)
For rotational motion,
$10R-fR=I\alpha$
$\Rightarrow (10-f)R=\frac{2}{3}m{R}^2.\frac{a}{R}$
$\Rightarrow (10-f)=\frac{2}{3}\times 2\times a=\frac{4}{3}a$ ....... (2)
From eq (1) and (2)
$\Rightarrow 20=\frac{10}{3}a$
$\Rightarrow a=6{\text{m/s}}^2$