Question

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. $24/n\, hr$
• B. $24\,n\, hr$
• C. $24/n^2\, hr$
• D. $24\, n^2\, hr$

Answer 1

The Correct Option is C

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 $T_{2}=\frac{T_{1}}{n^{2}}=\frac{24}{n^{2}} h$