Question

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours 30 minutes.

Answer 1

Correct answer is : 13 

By conservation of angular momentum

\(\mathrm{I}_{1} \omega_{1}=\mathrm{I}_{2} \omega_{2}\)

\(\left(\frac{2}{5} \mathrm{MR}^{2}\right) \frac{2 \pi}{\mathrm{T}_{1}}=\frac{2}{5} \mathrm{M}\left(\frac{3}{4} \mathrm{R}\right)^{2} \frac{2 \pi}{\mathrm{T}_{2}}\)

\(\frac{1}{\mathrm{~T}_{1}}=\frac{9}{16 \mathrm{~T}_{2}}\)

\(\frac{1}{\mathrm{~T}_{2}}=\frac{9}{16} \times \mathrm{T}_{1}=\frac{9}{16} \times 24 \mathrm{hr}=\frac{27}{2} \mathrm{hr}=13\ \mathrm{hr}\ 30\) mins.