1. Tardigrade
  2. Question
  3. Physics
  4. If the Earth were to suddenly contract to (1/n) th of its present radius without any change in its mass, the duration of the new day will be nearly

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

WBJEEWBJEE 2011System of Particles and Rotational Motion

Solution:

From the conservation of momentum, we have
$I_{1} \omega_{1}=I_{2} \omega_{2}$
Thus, we get $\frac{2}{5} M R^{2}\left(\frac{2 \pi}{T_{1}}\right)$ $=\frac{2}{5} M \frac{R^{2}}{n^{2}}\left(\frac{2 \pi}{T_{2}}\right)$
Hence, we get $T_{2}=\frac{T_{1}}{n^{2}}=\frac{24}{n^{2}} h$