Sankalp NEET Full Test-3 Question-17 Solution

Question: 17. 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) 100 days

(2) 105 days

(3) 115 days

(4) 108 days

Answer: Option (4)

Explanation:

Since no external torque acts on the Sun, its angular momentum is conserved. For a solid sphere of uniform density, the moment of inertia is

I = \frac{2}{5} M R^{2}

Angular momentum conservation gives:

I \omega = I' \omega'

If the radius doubles:

R' = 2R

Then the new moment of inertia becomes:

I' = \frac{2}{5} M (2R)^{2} = 4I

Thus,

I \omega = 4I \omega' \omega' = \frac{\omega}{4}

Since period T = \frac{2\pi}{\omega},

T' = 4T

Given the original period is:

T = 27\ \text{days}

Therefore,

T' = 4 \times 27 = 108\ \text{days}

Hence, the correct answer is Option (4).