Question

A tangential force $10\text{N}$ acts at the top of a thin spherical shell of mass $m\left(5\text{kg}\right)$ and radius $R\left(20\text{cm}\right)$. Find the acceleration of the shell if it rolls without slipping.

• A. $2{\text{m/s}}^2$
• B. $\frac{5}{12}{\text{m/s}}^2$
• C. $10{\text{m/s}}^2$
• D. $\frac{12}{5}{\text{m/s}}^2$

Answer 1

The correct option is D $\frac{12}{5}{\text{m/s}}^2$

Let $f$ be the friction force between the shell and the horizontal surface.


For translational motion,
$10+f=5a.....\left(i\right)$
For rotational motion,
$FR-fR=I\alpha$
$\Rightarrow (10-f)R=\frac{2M{R}^2}{3}\left(\frac{a}{R}\right)[\because R=20\text{cm}=0.2\text{m}]$
$\Rightarrow 10-f=\frac{2}{3}Ma=\frac{10}{3}a$
$\Rightarrow 10-f=\frac{10}{3}a---\left(ii\right)$

From equation (i) & (ii),
$a=\frac{20\times 3}{25}=\frac{12}{5}{\text{m/s}}^2$