Question

Total kinetic energy of a solid sphere of mass 1 kg rolling with velocity 1 m/s is

• A. $\frac{2}{5}J$
• B. $\frac{1}{2}J$
• C. $\frac{7}{10}J$
• D. $\frac{3}{5}J$

Answer 1

Answer: (C)

$\frac{7}{10}J$

Given,

$m=1kg$

$v=1m/s$

Total kinetic energy,

$K=\frac{1}{2}m{v}^2+\frac{1}{2}I{\omega }^2$. . . . . . . . .(1)

Where, Moment of inertia $I=\frac{2}{5}m{r}^2$ for pure rolling

$\omega =\frac{v}{r}$

From equation (1),

$K=\frac{1}{2}m{v}^2+\frac{1}{2}.\frac{2}{5}m{r}^2.\frac{v^2}{r^2}=\frac{7}{10}m{v}^2$

$K=\frac{7}{10}\times 1\times 1=\frac{7}{10}J$

The correct option is C.