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

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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.

Accepted Answer

Assuming the Sun to be a solid sphere, $I = \frac{2}{5}mR^{2}$

Using conservation of angular momentum, $l^{'}\omega^{'} = l\omega$

$$\begin{matrix} & \ \Rightarrow \frac{2}{5}m(2R)^{2} \times \frac{2\pi}{T^{'}} = \frac{2}{5}mR^{2} \times \frac{2\pi}{T} \\ & \ \Rightarrow T^{'} = 4T = 4 \times 27 = 108\text{~}\text{days}\text{~} \end{matrix}$$

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