Q.17 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 17 Solution

Topic: System of Particles and Rotational Motion · Official NTA Booklet Code 45

Question

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.

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Verified Against NTA Final Answer Key

Option (4) : 108 days

📚 System of Particles and Rotational Motion Easy

📋 Given Parameters & Problem Setup

Initial Rotation Period (T₁) 27 days

Radius Expansion Ratio (R₂ / R₁) 2 (radius expands to twice its present value)

Condition Expansion without any external influence (isolated system)

Geometry Sphere of uniform density (I = 2/5 M R²)

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The 30-Second Exam Hall Shortcut: ⚡ Angular Momentum R² Scaling Rule

⏱️ Save ~40 seconds

No external torque ⟹ L = I ω = const ⟹ T ∝ R² ⟹ T₂ = T₁ × (2)² = 27 × 4 = 108 days!

1 Notice: Expansion occurs without external influence (net external torque τ_ext = 0).

2 Conservation of angular momentum: L = I ω = constant.

3 Moment of inertia of sphere: I = (2/5) M R² ∝ R² (mass M is conserved).

4 Angular frequency: ω = 2π / T ⟹ T ∝ I ∝ R².

5 When radius doubles (R₂ = 2R₁), period scales by 2² = 4.

6 T₂ = 4 × 27 days = 108 days.

7 Select Option (4) in under 10 seconds!

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Why You Can 100% Trust This Shortcut: Law of Conservation of Angular Momentum (NCERT Physics · System of Particles and Rotational Motion: L = Iω = const).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Principle of Conservation of Angular Momentum

Since the Sun expands solely due to internal forces with zero external torque acting on it, its total angular momentum is strictly conserved.

\tau_{ext} = 0 \implies L_1 = L_2 \implies I_1 \omega_1 = I_2 \omega_2

• Angular speed is related to the period of rotation by ω = 2π / T.

Step 2

Relation Between Period and Radius

For a solid spherical body of uniform density and constant mass M, the moment of inertia is proportional to the square of its radius:

I = \frac{2}{5} M R^2 \implies I_1 \left(\frac{2\pi}{T_1}\right) = I_2 \left(\frac{2\pi}{T_2}\right) \implies \frac{T_2}{T_1} = \frac{I_2}{I_1} = \left(\frac{R_2}{R_1}\right)^2

• Given R₂ / R₁ = 2.

Step 3

Calculate New Period of Revolution

Substitute the given expansion factor and initial period:

T_2 = T_1 \times (2)^2 = 27\text{ days} \times 4 = 108\text{ days}

• Matches Option (4) exactly.

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Rounding error or approximation.

⚠️

Student Fallacy (Why candidates pick this trap): Rounding 108 down to 100.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Arbitrary distractor.

⚠️

Student Fallacy (Why candidates pick this trap): Calculation slip during multiplication.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Overestimation.

⚠️

Student Fallacy (Why candidates pick this trap): Adding days instead of multiplying by 4.

4 D

✓ 100% Correct

Verdict & Scientific Reason:

100% exact. T ∝ R² ⟹ T₂ = 27 × 2² = 108 days.

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Why this is airtight: None; textbook angular momentum conservation.

⚠️

NTA Trap Alert: Linear vs. Quadratic Radius Scaling

Students sometimes think T ∝ R, concluding T₂ = 27 × 2 = 54 days. Because moment of inertia depends on R², period scales as R², quadrupling the time.

🛡️ How to avoid the -1 mark: Remember: Inertia has R SQUARED (I = 2/5 M R²) ⟹ Period scales by 2² = 4!

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Core NEET Syllabus Standard

NEET Physics Core Syllabus · System of Particles and Rotational Motion Standard Benchmark

Core Scientific Principle Tested:

"In the absence of external torque, I₁ ω₁ = I₂ ω₂ ⟹ T ∝ R² for constant mass."

Syllabus Focus: Conservation of Angular Momentum

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Radius Doubles ⟹ Inertia Quadruples ⟹ 4 × 27 = 108 days!

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NEET 2025 Physics Question 17 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Angular Momentum R² Scaling Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Principle of Conservation of Angular Momentum

Relation Between Period and Radius

Calculate New Period of Revolution

360° Option Elimination Engine Key Feature

NTA Trap Alert: Linear vs. Quadratic Radius Scaling

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — System of Particles and Rotational Motion

Moment of Inertia Difference for Attached Solid Spheres via Parallel Axis Theorem

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