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. [2025]

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Solution

Q.
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. [2025]

1 115 days

2 108 days

3 100 days

4 105 days

Ans.
(2)

$T_{1} = 27$ days, $R_{1} = R,$ $R_{2} = 2 R$

By conservation of angular momentum

$I_{1} ω_{1} = I_{2} ω_{2}$

$\frac{2}{5} m R_{1}^{2} \times \frac{2 π}{T_{1}} = \frac{2}{5} m R_{2}^{2} \times \frac{2 π}{T_{2}}$

$\frac{R^{2}}{27} = \frac{4 R^{2}}{T_{2}} \Rightarrow T_{2} = 27 \times 4 = 108 days$

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