If the earth were to suddenly contract to fra | vedclass

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(C) According to the law of conservation of angular momentum,the angular momentum of the system remains conserved because no external torque acts on t

Vedclass · Accepted Answer

$\frac{24}{n^2} \ hr$

Vedclass · Answer

(C) According to the law of conservation of angular momentum,the angular momentum of the system remains conserved because no external torque acts on the Earth.$L_i = L_f$$I_1 \omega_1 = I_2 \omega_2$Since the Earth is a solid sphere,its moment of inertia is $I = \frac{2}{5}MR^2$. The angular velocity is $\omega = \frac{2\pi}{T}$.Substituting these into the conservation equation:$\frac{2}{5}MR^2 \left(\frac{2\pi}{T_1}\right) = \frac{2}{5}M\left(\frac{R}{n}\right)^2 \left(\frac{2\pi}{T_2}\right)$$R^2 \left(\frac{1}{T_1}\right) = \frac{R^2}{n^2} \left(\frac{1}{T_2}\right)$Given $T_1 = 24 \ hr$,we get:$\frac{1}{24} = \frac{1}{n^2 T_2}$$T_2 = \frac{24}{n^2} \ 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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