Q.15 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 15 Solution

Topic: Gravitation · Official NTA Booklet Code G5

Question

Two bodies of mass m and 9m are placed at a distance R. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (G = gravitational constant):

✓

Verified Against NTA Final Answer Key

Option (4) : -16 Gm / R

📚 Gravitation Medium

📋 Given Parameters & Problem Setup

Body 1 Mass m

Body 2 Mass 9m

Separation R

Location Where gravitational field equals zero (Neutral Point)

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The 30-Second Exam Hall Shortcut: ⚡ Square-Root Mass Ratio Neutral Point Shortcut

⏱️ Save ~50 seconds

Neutral distance from m is x = R / (1 + √(9m/m)) = R / (1 + 3) = R/4! Potential V = -Gm/(R/4) - 9Gm/(3R/4) = -4 - 12 = -16 Gm/R in 20 seconds!

1 Gravitational field balances where GM₁/x² = GM₂/(R-x)², meaning distance scales with √mass: x₁ / x₂ = √(m) / √(9m) = 1 / 3.

2 Divide distance R into 1 + 3 = 4 parts: x = R/4 from m, and (3R/4) from 9m.

3 Compute potential from mass m: V₁ = -Gm / (R/4) = -4 Gm / R.

4 Compute potential from mass 9m: V₂ = -G(9m) / (3R/4) = -(9 × 4 / 3) Gm / R = -12 Gm / R.

5 Sum scalar potentials: V_total = -4 - 12 = -16 Gm / R. Instant lock on Option (4)!

🛡️

Why You Can 100% Trust This Shortcut: Fundamental Gravitational Mechanics · Potential and Field Superposition (Neutral point distance: x = R / (1 + √(M₂/M₁))).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Locating the Gravitational Neutral Point

Let the neutral point P be located at distance x from mass m and (R - x) from mass 9m along the line joining them. At P, the net gravitational field is zero:

E_{\text{net}} = \frac{G m}{x^2} - \frac{G (9m)}{(R - x)^2} = 0 \implies \frac{1}{x^2} = \frac{9}{(R - x)^2}

Step 2

Square Root Solution for Distance x

Taking the square root on both sides (since distance must lie between the masses):

\frac{1}{x} = \frac{3}{R - x} \implies R - x = 3x \implies 4x = R \implies x = \frac{R}{4}

Step 3

Distances from Both Masses

The distances from the respective masses are:

r_1 = x = \frac{R}{4}, \qquad r_2 = R - x = R - \frac{R}{4} = \frac{3R}{4}

Step 4

Gravitational Potential Superposition

Gravitational potential is a scalar quantity. The total potential V at point P is the algebraic sum of the potentials due to m and 9m:

V = -\frac{G m}{r_1} - \frac{G (9m)}{r_2} = -\frac{G m}{\frac{R}{4}} - \frac{9 G m}{\frac{3R}{4}} = -\frac{4Gm}{R} - \frac{36Gm}{3R} = -\frac{4Gm}{R} - \frac{12Gm}{R} = -\frac{16Gm}{R}

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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 (1)

✗ Incorrect

Verdict & Scientific Reason:

Overestimates negative potential magnitude.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate incorrectly placed neutral point at R/5 and calculated -5 - 15 = -20.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Underestimates potential magnitude.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate subtracted potentials instead of adding negative scalar contributions.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Represents only the contribution of the larger 9m mass, ignoring mass m.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate calculated V₂ = -12 Gm/R and forgot to add V₁ = -4 Gm/R.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value: scalar sum of -4 Gm/R and -12 Gm/R at the neutral point.

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Why this is airtight: None. Candidate executed both field-balance and potential-superposition steps correctly.

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NTA Trap Alert: Using Mass Ratio Instead of Square Root of Mass Ratio for Field Balance

Hasty students write x / (R - x) = 1/9 instead of taking the square root 1/3. This places x at R/10 and leads to completely wrong potentials.

🛡️ How to avoid the -1 mark: Remember: Gravitational field is inverse-square (1/r²), so neutral distance ratio scales with the SQUARE ROOT of mass (√1 : √9 = 1 : 3).

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Gravitation Standard Benchmark

Core Scientific Principle Tested:

"Gravitational field is a vector (E = -dV/dr), while potential is an additive negative scalar (V = -GM/r)."

Syllabus Focus: Gravitational Field, Potential, and Neutral Points

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 15 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Square-Root Mass Ratio Neutral Point Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Locating the Gravitational Neutral Point

Square Root Solution for Distance x

Distances from Both Masses

Gravitational Potential Superposition

360° Option Elimination Engine Key Feature

NTA Trap Alert: Using Mass Ratio Instead of Square Root of Mass Ratio for Field Balance

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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