Question

A metal sphere of mass m , radius r and specific heat c is rotated about an axis passing through its centre at a speed of n rotations per second. It is suddenly stopped and 50% of its energy is used in increasing its temperature. Then rise in temperature of the sphere is

• A. $\frac{2}{5}\frac{{\pi }^2{n}^2{r}^2}{c}$
• B. $\frac{1}{10}\frac{{\pi }^2{n}^2}{r^{2}c}$
• C. $\frac{7}{8}\pi r^2{n}^{2}c$
• D. $5{\left[\frac{\pi rn}{14c}\right]}^2$

Answer 1

The correct option is A $\frac{2}{5}\frac{{\pi }^2{n}^2{r}^2}{c}$

Here, $\frac{50}{100}$ (KE of rotation) = cm$\theta$
$\frac{1}{2}\left(\frac{1}{2}I{\omega }^2\right)=\frac{1}{4}\left(\frac{2}{5}m{r}^2\right)(2\pi n{)}^2=cm\theta$
$\theta =\frac{2}{5}\frac{{\pi }^2{n}^2{r}^2}{c}$