Question

A solid sphere of mass $2\text{kg}$ and diameter $10\text{cm}$ is rolling without slipping at a speed of $5{\text{ms}}^{-1}.$ The rotational kinetic energy of the sphere will be

• A. $10\text{J}$
• B. $30\text{J}$
• C. $50\text{J}$
• D. $70\text{J}$

Answer 1

The correct option is A $10\text{J}$

Rotational kinetic energy, $K{E}_{Rot}=\frac{1}{2}{I}_{\text{CM}}{\omega }^2$
Moment of inertia of the solid sphere about the axis passing through it's $\text{COM}$ is:
$I_{\text{CM}}=\frac{2}{5}m{r}^2,m=2\text{kg},r=5\text{cm}=0.05\text{m}$
Applying condition of pure rolling$(v=r\omega )$
$K{E}_{Rot}=\frac{1}{2}(\frac{2}{5}\times 2\times (0.05{)}^2){\omega }^2$
$K{E}_{Rot}=\frac{2}{5}\times (0.05{)}^2\times \frac{v^2}{{0.05}^2}$
$\therefore K{E}_{Rot}=\frac{2}{5}\times 25=10\text{J}$