Question

If the radius of earth contracts $\frac{1}{n}$ of its present value, the length of the day will be approximately

• A. $\frac{24}{n}h$
• B. $\frac{24}{n^2}h$
• C. $24nh$
• D. $24n^{2}h$

Answer 1

The correct option is B

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

Conservation of angular momentum $L=I\omega =\frac{2}{5}M{R}^2\times \frac{2\pi }{T}=constant$

$\therefore T\propto R^2\left[IfMremainssame\right]\Rightarrow \frac{T_2}{T_1}={\left(\frac{R_2}{R_1}\right)}^2={\left(\frac{\frac{R}{n}}{R}\right)}^2=\frac{1}{n^2}\Rightarrow T_2=\frac{24}{n^2}hr[As{T}_1=24hr]$