Physics Q17 – NEET-UG 2025

Home Physics Rotational MotionQuestion #438

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.

Clue 1 of 3: Conservation Principle

When there is no external torque acting on a system, its angular momentum remains conserved.

🧠 Full Solution Path

● Video Walkthrough

Step 1: Apply Conservation of Angular Momentum✦ Active

Since there is no external influence, the angular momentum ( $L$ ) of the Sun is conserved. The angular momentum is given by $L = I ω$ , where $I$ is the moment of inertia and $ω$ is the angular velocity. For a solid sphere, $I = \frac{2}{5} M R^{2}$ , and $ω = \frac{2 π}{T}$ .

L_{1} = L_{2} ⟹ I_{1} ω_{1} = I_{2} ω_{2}

Step 2: Substitute Expressions and Simplify○ Expand

Substitute the expressions for $I$ and $ω$ into the conservation equation. The mass $M$ remains constant.

\frac{2}{5} M R_{1}^{2} (\frac{2 π}{T_{1}}) = \frac{2}{5} M R_{2}^{2} (\frac{2 π}{T_{2}})

R_{1}^{2} \frac{1}{T_{1}} = R_{2}^{2} \frac{1}{T_{2}}

\frac{T_{2}}{T_{1}} = {(\frac{R_{2}}{R_{1}})}^{2}

💡 Teacher's Secret Hint

Remember that the mass of the Sun does not change during expansion.

Step 3: Calculate the New Period○ Expand

Given $T_{1} = 27$ days and $R_{2} = 2 R_{1}$ . Substitute these values into the derived relation.

T_{2} = T_{1} {(\frac{2 R_{1}}{R_{1}})}^{2} = T_{1} (2)^{2} = 4 T_{1}

T_{2} = 4 \times 27 days = 108 days

💡 Teacher's Secret Hint

Pay attention to the squaring of the radius ratio.

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Physics Question 17 – NEET-UG 2025

Clue 1 of 3: Conservation Principle

🧠 Full Solution Path