Question

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

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

Answer 1

The correct option is B $5:7$

In rolling motion the translational kinetic energy is equal to

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

In rolling motion the rotational kinetic energy is equal to

$K_r=\frac{1}{2}I{\omega }^2$

$K_r=\frac{1}{2}\left(\frac{2}{5}m{r}^2\right)\left(\frac{v^2}{r^2}\right)$

$K_t+K_r=\frac{1}{2}m{v}^2+\frac{1}{2}\left(\frac{2}{5}m{r}^2\right)\left(\frac{v^2}{r^2}\right)$

$K_t+K_r=\frac{7}{10}m{v}^2$

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