Question

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $\left(K_t\right)$ as well as rotational kinetic energy $\left(K_r\right)$ simultaneously. The ratio $K_t:(K_t+K_r)$ for the sphere is?

• A. $10:7$
• B. $7:10$
• C. $2:5$
• D. $5:7$

Answer 1

The correct option is D $5:7$

$K_t=\frac{1}{2}m{v}_2$

$K_r=\frac{1}{2}IW=\frac{1}{2}\times \frac{2}{5}\times m{r}^2\times \frac{v^2}{r^2}$

$=\frac{1}{5}m{v}^2$

$\Rightarrow \frac{K_t}{K_t+K_r}=\frac{1_{/2}m{v}^2}{\left(\frac{1}{2}+\frac{1}{5}\right)m{v}^2}=\frac{1_{/2}}{7_{/10}}=\frac{5}{7}$

Option 4.