The Sun rotates around its centre once in 27 days. What will be the...

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.

Options

A100 days
B105 days
C115 days
D108 days

Correct answer

D. 108 days

Step-by-step solution

Angular Momentum conservation

\begin{array}{l|l} \mathrm{I}_1\omega_1=\mathrm{I}_2 \omega_2 & \mathrm{M}=\text{ same } \\ \omega_2=\frac{\omega_1}{4} & \mathrm{R}_2=2 \mathrm{r}_1\\ T=\frac{2 \pi}{\omega} & \mathrm{I} \propto \mathrm{r}^2\\ & \mathrm{I}_2=4 \mathrm{I}_1 \\ & \mathrm{ T}_1=27 \text{ day } \end{array}

\begin{aligned} & \mathrm{T}_2=4\mathrm{ T}_1=4 \times 27 \\ & \mathrm{ T}_2=108\text{ days }\end{aligned}

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