Explanation

(c) From law of conservation of angular momentum,
$J = I\omega =$constant
$\therefore$ $I_{1}\omega_{1} = I_{2}\omega_{2}$
where $I$ is moment of inertia and $\omega$ the angular velocity.
Moment of inertia of earth assuming it be a sphere of radius
$R = \frac{2}{5}\ MR^{2}$
Also $\omega = \frac{2\pi}{T}$
$\therefore$ $\left( \frac{2}{5}MR_{1}^{2} \right)\left( \frac{2\pi}{T_{1}} \right) = \left( \frac{2}{5}MR_{2}^{2} \right)\left( \frac{2\pi}{T_{2}} \right)$
$\Rightarrow$ $\frac{R_{1}^{2}}{T_{1}} = \frac{R_{2}^{2}}{T_{2}}$
$\Rightarrow$ $\frac{R_{1}^{2}}{24} = \left( \frac{R_{1}}{2} \right)^{2} \times \frac{1}{T_{2}}$
$\Rightarrow$ $T_{2} = 6$h