Question

If the earth suddenly becomes a thin shell of same radius the length of a day becomes

• A. $24hr$
• B. $6hr$
• C. $\frac{7}{2}hr$
• D. $40hr$

Answer 1

The correct option is A $24hr$

Moment of inertia of sphere $=\frac{2}{5}M{R}^2$

Moment of inertia of shell $=\frac{2}{3}M{R}^2$

$\because T^2\propto I$

$\frac{T_{sphere}}{T_{shell}}=\frac{\sqrt{\frac{2}{5}}M{R}^2}{\sqrt{\frac{2}{3}}M{R}^2}$

$\frac{24}{T_{shell}}=\sqrt{\frac{3}{5}}$

$T_{shell}=30hours\left(Approx\right)$