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10-1.Thermometry, Thermal Expansion and Calorimetry
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If the earth suddenly stops revolving and all its rotational $KE$ is used up in raising its temperature and if $'s'$ is taken to be the specific heat of the earth's material, the rise of temperature of the earth will be : ( $R -$ radius of the earth and $\omega =$ its angular velocity, $J =\,Joule$ constant)
A
$\frac{{{R^2}{\omega ^2}}}{{5Js}}$
B
$\frac{{{R^2}{\omega ^2}}}{{5J}}$
C
$\frac{{{R^2}\omega }}{{5Js}}$
D
$\frac{{{R^2}{\omega ^2}}}{{5s}}$
Solution
$\frac{\mathrm{K}_{\mathrm{R}}}{\mathrm{J}}=\frac{\frac{1}{2} \mathrm{I} \omega^{2}}{\mathrm{J}}=\mathrm{Ms} \theta$
or $\frac{1}{2} \times \frac{2}{5} \frac{\mathrm{MR}^{2} \omega^{2}}{\mathrm{J}}=\mathrm{Ms} \theta$
$\therefore \theta=\frac{R^{2} \omega^{2}}{5 S J}$
Standard 11
Physics
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