A metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $f$ rotations per second. It is suddenly stopped at $50\%$ of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is
A metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $f$ rotations per second. It is suddenly stopped at $50\%$ of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is
- A
$\frac{{2{\pi ^2}{f^2}{r^2}}}{{5S}}$
- B
$\frac{{{\pi ^2}{f^2}}}{{10{r^2}S}}$
- C
$\frac{7}{8}\pi {r^2}{f^2}S$
- D
$\frac{{5{{\left( {\pi rf} \right)}^2}}}{{14S}}$
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