Question

A solid sphere of mass $500\text{g}$ and radius $10\text{cm}$ rolls without slipping with a velocity of $20\text{cm/s}$. The total $K.E$. of the sphere is nearly

• A. $0.001\text{J}$
• B. $0.014\text{J}$
• C. $0.14\text{J}$
• D. $1.4\text{J}$

Answer 1

The correct option is B $0.014\text{J}$

Total $K.E$, includes both Rotational and Translational $K.E$ $=\frac{1}{2}I{\omega }^2+\frac{1}{2}m{v}^2=\frac{1}{2}\times \frac{2}{5}m{r}^2{\omega }^2+\frac{1}{2}m{v}^2$
As, $I_{\text{sphere}}=\frac{2}{5}m{r}^2$, since it is pure rolling, $v=\omega r$.

Total $K.E=\frac{1}{5}m{v}^2+\frac{1}{2}m{v}^2=\frac{7}{10}m{v}^2$
$=\frac{7}{10}\times \frac{500}{1000}\times {\left(\frac{1}{5}\right)}^2=0.014\text{J}$

$($As $20\text{cm/s}=\frac{1}{5}\text{m/s})$
Hence the correct answer is option B