Question

If rotation of the earth stopped suddenly then find the rise in temperature of the earth. Assume total rational energy is converted into thermal energy (specific heat of earth $=0.15$, radius of earth $6400km$)

• A. ${78.76}^{\circ }C$
• B. ${6.876}^{\circ }C$
• C. ${68.76}^{\circ }C$
• D. ${0.6876}^{\circ }C$

Answer 1

The correct option is A ${78.76}^{\circ }C$

The Rotation Energy of the body is given as

$=\frac{1}{2}I{\omega }^2$

The moment of inertia of the solid spherical body is

$I=\frac{2}{5}m{r}^2$

The angular velocity of the body is given as:

$\omega =\frac{2\pi }{T}$

The thermal energy of the body is given by

= $mc\Delta T=\frac{1}{2}\left(\frac{2}{5}m{r}^2\right)\frac{2\pi }{24\times 3600}$

solving above equation:

$\Delta T={78.76}^{o}C$