Question

If earth shrinks to $\frac{1}{64}$ of its volume with mass remaining same, duration of day will be

• A. 1.5 h
• B. 3 h
• C. 4.5 h
• D. 6 h

Answer 1

The correct option is A 1.5 h

$\begin{array}{c}Ifthevolumeofearthsuddenlyshirnksto\frac{1}{64}ofitsoriginalvolume\\ then,theradiusoftheearthwilldecreaseto\frac{1}{4}ofitsoriginalradius.\\ I\overline{\omega }=cons\tan t\\ \Rightarrow \left(\frac{2}{5}M{R}^2\right)\left(\frac{2\pi }{T}\right)=\frac{2}{5}M{\left(\frac{R}{4}\right)}^2\frac{2\pi }{T^{\prime }}\\ \Rightarrow \frac{1}{T}=\frac{1}{16T^{\prime }}\\ \Rightarrow T^{\prime }=\frac{T}{15}\\ =\frac{24}{16}hr=1.5hr\end{array}$

Hence,

option $\left(A\right)$ is correct answer.