The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun

Question

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere uniform density.

Professor PC Thomas Classes · Answer

(b) : $T_1=27$ days, $R_1=R, R_2=2 R$ \ By conservation of angular momentum \ $ \begin{aligned} & I_1 \omega_1=I_2 \omega_2 \ & \frac{2}{5} m R_1^2 	imes \frac{2 \pi}{T_1}=\frac{2}{5} m R_2^2 	imes \frac{2 \pi}{T_2} \ & \frac{R^2}{27}=\frac{4 R^2}{T_2} ; T_2=27 	imes 4=108 	ext { days } \end{aligned} $