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 p…

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 of uniform density.

1. A. 100 days
2. B. 105 days
3. C. 115 days
4. D. 108 days (Correct answer)

Correct Answer

Option D — 108 days

Detailed Solution & Explanation

The correct answer is 108 days.

Key Points

• With no external torque, angular momentum is conserved: $I'\omega'=I\omega$.
• For a solid sphere $I=\dfrac{2}{5}mR^2$, so $I\propto R^2$ and $\omega=\dfrac{2\pi}{T}$.
• $\dfrac{2}{5}m(2R)^2\dfrac{2\pi}{T'}=\dfrac{2}{5}mR^2\dfrac{2\pi}{T}\;\Rightarrow\;T'=4T$.
• $T'=4\times 27=108$ days.