Q.14 Physics ⭐ 360° Option Elimination Active

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NEET 2026 Physics Question 14 Solution

Topic: Gravitation · Official NTA Booklet Code 50

Question

In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to:

✓

Verified Against NTA Final Answer Key

Option (2) : T is proportional to R^{3/2}

📚 Gravitation Easy

📋 Given Parameters & Problem Setup

Planetary Orbit Circular orbit of radius R

Time Period Period of revolution T

Governing Law Newton's Law of Universal Gravitation / Kepler's Third Law

⚡

The 30-Second Exam Hall Shortcut: ⚡ Kepler's Harmonic Law Direct Rule

⏱️ Instant recall.

Square of period is proportional to cube of radius

1 State Kepler's 3rd Law: T^2 is proportional to R^3.

2 Take square root on both sides: T is proportional to (R^3)^(1/2) = R^(3/2).

3 Direct identification in 5 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Equating gravitational pull GMm/R^2 to centripetal force m*(2pi/T)^2*R gives T = (2pi / sqrt(GM)) * R^(3/2), proving the power 3/2 rigorously.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulate Dynamic Equilibrium for Circular Planetary Orbit

For a planet of mass m orbiting a star of mass M at radius R, gravitational attraction provides the necessary centripetal force:

F_g = F_c \implies \frac{G M m}{R^2} = m \omega^2 R

• Mass of the planet m cancels from both sides.
• G is the universal gravitational constant, and M is the solar mass.

Step 2

Relate Angular Frequency to Orbital Period

Substitute omega = 2pi / T into the dynamic balance:

\frac{G M}{R^3} = \omega^2 = \left(\frac{2\pi}{T}\right)^2 = \frac{4\pi^2}{T^2}

• Cross-multiply to isolate T^2: T^2 = \left(\frac{4\pi^2}{G M}\right) R^3.
• This is Kepler's Third Law: T^2 \propto R^3.

Step 3

Extract Proportionality for Time Period T

Take the square root of both sides to obtain the explicit power of R:

T = \left(\frac{2\pi}{\sqrt{G M}}\right) R^{3/2} \implies T \propto R^{3/2}

• The orbital period scales as R^(3/2) (or R^1.5).
• Matches Option (2) 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 Option (1)

✗ Incorrect

Verdict & Scientific Reason:

Applies to pendulum time period, not planetary orbits.

⚠️

Student Fallacy (Why candidates pick this trap): Confuses simple pendulum period T = 2pi*sqrt(L/g) with Kepler's law.

Note: In gravitation, force scales as 1/R^2, which leads to R^(3/2), not R^(1/2).

2 Option (2)

✓ 100% Correct

Verdict & Scientific Reason:

Canonical statement of Kepler's Third Law; confirmed by Official NTA Final Answer Key.

💡

Why this is airtight: Direct derivation from gravitational centripetal equilibrium.

Note: Exact physics.

3 Option (3)

✗ Incorrect

Verdict & Scientific Reason:

Areal velocity confusion.

⚠️

Student Fallacy (Why candidates pick this trap): Confuses Kepler's second law areal parameters with orbital period.

Note: T scales with R^1.5, never R^2.

4 Option (4)

✗ Incorrect

Verdict & Scientific Reason:

Omitted square root.

⚠️

Student Fallacy (Why candidates pick this trap): Remembers T^2 ~ R^3 but forgets to take the square root to isolate T.

Note: T^2 is proportional to R^3, meaning T is proportional to R^(3/2).

⚠️

NTA Trap Alert: Confusing T^2 ~ R^3 with T ~ R^3

Students frequently memorize "Kepler's law relates period and cube of radius" and hastily select R^3 without isolating the power of T.

🛡️ How to avoid the -1 mark: Always isolate the exact requested variable: T = (R^3)^(1/2) = R^(3/2).

📖

Core NEET Syllabus Standard

NEET UG Physics Core Standards · Gravitation Standard Benchmark

Core Scientific Principle Tested:

"Kepler's Third Law (Law of Periods): The square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of its orbit: T^2 = k * R^3."

Syllabus Focus: Kepler's Laws of Planetary Motion

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2026 Physics Question 14 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Kepler's Harmonic Law Direct Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulate Dynamic Equilibrium for Circular Planetary Orbit

Relate Angular Frequency to Orbital Period

Extract Proportionality for Time Period T

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing T^2 ~ R^3 with T ~ R^3

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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