Question

The total energy of a solid. sphere of mass 800 g which rolls without slipping with a constant velocity of $5m{s}^{-1}$ along a straight line is

• A. 5.25 J
• B. 3.25 J
• C. 0.25 J
• D. 1.25 J
• E. 0.626 J

Answer 1

The correct option is A 5.25 J

The kinetic energy $K=\frac{1}{2}I{\omega }^2$

For solid sphere $I_{CM}=\frac{2}{5}m{r}^2$

$K{E}_{total}=\frac{1}{2}\left(\frac{2}{5}m{r}^2\right){\omega }^2+\frac{1}{2}m{r}^2{\omega }^2$

$=\frac{1}{5}=m{r}^2{\omega }^2+\frac{1}{2}m{r}^2{\omega }^2$

$=\frac{7}{10}m{r}^2{\omega }^2$ $(\because v=r\omega )$

$K{E}_{total}=\frac{7}{10}m{v}^2=\frac{7}{10}\times \frac{300}{1000}\times 5^2$

$=0.7\times 0.3\times 25=5.25J$