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
A) $\frac{24}{n}h$
B) $24n\ h$
C) $\frac{24}{n^{2}}h$
D) $24n^{2}h$
Explanation
(c) ${I_{1}\omega}_{1} = I_{2}\omega_{2}$
$\ \ \ \ \ \ \ \ \ \ \frac{2}{5}{MR}^{2}\left( \frac{2\pi}{T_{1}} \right) = \frac{2}{5}M \bullet \frac{R^{2}}{n^{2}}\left( \frac{2\pi}{T_{2}} \right)$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T_{2} = \frac{T_{1}}{n^{2}} = \frac{24}{n^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.