If the earth were to suddenly contract to 1/n | vedclass

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(C) According to the principle of conservation of angular momentum,the angular momentum $L = I\omega$ remains constant because no external torque acts

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$24/n^2$

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(C) According to the principle of conservation of angular momentum,the angular momentum $L = I\omega$ remains constant because no external torque acts on the system.$I_1 \omega_1 = I_2 \omega_2$Since the earth is a sphere,its moment of inertia is $I = \frac{2}{5}MR^2$. The angular velocity is $\omega = \frac{2\pi}{T}$,where $T$ is the duration of the day.Substituting these into the conservation equation:$\frac{2}{5} MR^2 	imes \frac{2\pi}{24} = \frac{2}{5} M \left(\frac{R}{n}ight)^2 	imes \frac{2\pi}{T'}$Canceling common terms $\frac{2}{5} M$ and $2\pi$ from both sides:$R^2 	imes \frac{1}{24} = \frac{R^2}{n^2} 	imes \frac{1}{T'}$Solving for $T'$:$T' = \frac{24}{n^2} 	ext{ hours}$

If the earth were to suddenly contract to $1/n^{th}$ of its present radius without any change in its mass,the duration (in $hrs.$) of the new day will be nearly

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