Question

If the mass of earth and radius suddenly become $2times$ and $1/4^{th}$ of the present value, the length of the day becomes:

• A. $24h$
• B. $6h$
• C. $3/2h$
• D. $3h$

Answer 1

The correct option is D $3h$

If mass of earth becomes $2$ times and radius of earth becomes $\frac{1}{4}$ of the present value moment of inertia of earth $I=\frac{2}{5}{mR}^2$ becomes $\frac{1}{8}$ of the present value. As no external torque acting on the earth its angular momentum $L=Iw=I\frac{2\pi }{T}$ remains constant. As I becomes $\frac{1}{8}$ of present value so length of the day $T$ becomes $\frac{1}{8}$ of present day or $3$ hours.

Correct option (D).