Question

A metal sphere of 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 the rise in temperature of the sphere is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

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