If the Earth were to suddenly contract to fra | vedclass

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(C) According to the law of conservation of angular momentum, since no external torque acts on the Earth, the angular momentum remains constant: $L_1

Vedclass · Accepted Answer

$24 / n^2 	ext{ hr}$.

Vedclass · Answer

(C) According to the law of conservation of angular momentum, since no external torque acts on the Earth, the angular momentum remains constant: $L_1 = L_2$.Since $L = I\omega$, we have $I_1 \omega_1 = I_2 \omega_2$.The moment of inertia of a solid sphere is $I = \frac{2}{5}MR^2$.Let $R_1 = R$ and $R_2 = \frac{R}{n}$.Substituting these into the equation: $\frac{2}{5}MR^2 \left(\frac{2\pi}{T_1}ight) = \frac{2}{5}M\left(\frac{R}{n}ight)^2 \left(\frac{2\pi}{T_2}ight)$.Simplifying the equation: $R^2 \left(\frac{1}{T_1}ight) = \frac{R^2}{n^2} \left(\frac{1}{T_2}ight)$.Therefore, $T_2 = \frac{T_1}{n^2}$.Given the initial duration of the day $T_1 = 24 	ext{ hr}$, the new duration is $T_2 = \frac{24}{n^2} 	ext{ hr}$.

If the Earth were to suddenly contract to $\frac{1}{n}$ th of its present radius without any change in its mass, the duration of the new day will be nearly

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