Question

A uniform sphere of mass $200g$ rolls without slipping on a plane surface so that its centre moves at a speed of $2.00cm/s$. Find its kinetic energy.

• A. $5.6\times {10}^{-5}J$
• B. $6.6\times {10}^{-5}J$
• C. $5.6\times {10}^{-6}J$
• D. $6.6\times {10}^{-6}J$

Answer 1

The correct option is A $5.6\times {10}^{-5}J$

As the sphere rolls without slipping on the plane surface, its angular speed about the centre is = $\omega =\frac{V_{cm}}{r}$ The kinetic energy is
$K=\frac{1}{2}{I}_{cm}{\omega }^2+\frac{1}{2}M{v}_{cm}^2=\frac{1}{2}\frac{2}{5}m{r}^2{\omega }^2+\frac{1}{2}M{v}_{cm}^2$
= $\frac{1}{5}M{V}_{cm}^2+\frac{1}{2}M{v}_{cm}^2=\frac{7}{10}M{V}_{cm}^2=\frac{7}{10}\left(0.200kg\right)(0.02m/s{)}^2=$$5.6\times {10}^{-5}J$