Question

A metal sphere of radius r and specific heat S 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. $\frac{2\pi^{2}n^{2}r^{2}}{5S}$
• B. $\frac{\pi^{2}n^{2}}{10r^{2}S}$
• C. $\frac{7}{8}$pr²n²S
• D. $\frac{5(\pi rn)^{2}}{14S}$

Answer 1

Answer: (A)

$\frac{2\pi^{2}n^{2}r^{2}}{5S}$

Answer 2

I = $\frac{2}{5}$ mr², w = 2pn.

k = $\frac{1}{2}$ Iw² = $\frac{1}{2}$ × $\frac{2}{5}$ mr² × 4p² n²

= $\frac{4}{3}$ p² mr²n²

Dq = $\frac{\Delta Q}{mS}$ = $\frac{k/2}{mS}$ = $\frac{2}{5}$ $\frac{\pi^{2}mr^{2}n^{2}}{mS}$ = $\frac{2\pi^{2}r^{2}n^{2}}{5S}$