Question

If the earth suddenly stops revolving and all its rotational $KE$ is used up in rising its temperature, the rise in temperature of earth will be ($R$=radius of earth and $\omega$ its angular velocity, $s$=average specific heat of material of earth and $J$=the mechanical equivalent of heat)

• A. $\frac{R^2{\omega }^2}{5Js}$
• B. $\frac{5R^2{\omega }^2}{Js}$
• C. $\frac{R^2{\omega }^{2}J}{5s}$
• D. $\frac{5R^2{\omega }^{2}J}{s}$

Answer 1

The correct option is A $\frac{R^2{\omega }^2}{5Js}$

Kinetic energy of earth= $\frac{1}{2}I{\omega }^2$
considering earth as solid sphere,
$I=\frac{2}{5}\left(m{R}^2\right)$.
Kinetic energy =$\frac{1}{2}\frac{2}{5}\left(m{R}^2\right){\omega }^2$.
Given that if this energy converted to raise the temperature,
$mJs\Delta T=\frac{1}{5}\left(m{R}^2\right){\omega }^2$.
$\Rightarrow \Delta T=\frac{R^2{\omega }^2}{5Js}$