Q.32 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 32 Solution

Topic: Gravitation · Official NTA Booklet Code 45

Question

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is:

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Verified Against NTA Final Answer Key

Option (2) : 27 N

📚 Gravitation Easy

📋 Given Parameters & Problem Setup

Surface Weight (W₀ = mg) 48 N

Height Above Surface (h) R / 3 (where R is the radius of the Earth)

Target Variable Gravitational force (weight W') at height h

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The 30-Second Exam Hall Shortcut: ⚡ Inverse-Square Distance Scaling Rule

⏱️ Save ~35 seconds

Distance from center r = R + R/3 = 4R/3 ⟹ g' = g / (4/3)² = (9/16) g ⟹ W' = 48 × (9/16) = 27 N!

1 CRITICAL RULE: Height h = R/3 is NOT small compared to R (cannot use approximation g' ≈ g(1 - 2h/R)).

2 Calculate total radial distance from Earth’s center: r = R + h = R + R/3 = (4/3) R.

3 Gravitational force varies inversely with the square of distance: W' ∝ 1 / r².

4 Ratio: W' / W₀ = [R / (4/3 R)]² = (3/4)² = 9 / 16.

5 Multiply by surface weight: W' = 48 N × (9 / 16) = 3 × 9 = 27 N.

6 Select Option (2) in under 15 seconds!

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Why You Can 100% Trust This Shortcut: Newton’s Law of Universal Gravitation (NCERT Physics · Gravitation: F = GMm/r²).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Identify Radial Distance from Center of Earth

Gravitational attraction acts from the center of mass of the Earth. At a height h above the surface, the distance from the center is:

r = R + h = R + \frac{R}{3} = \frac{4}{3}R

• Because h is comparable to R, the exact inverse-square law must be applied.

Step 2

Formulate Exact Gravitational Force Equation

On the surface, the force is W₀ = G M m / R² = 48 N. At height h, the force is:

W' = \frac{G M m}{r^2} = \frac{G M m}{\left(\frac{4}{3}R\right)^2} = \frac{G M m}{R^2} \times \frac{9}{16} = W_0 \times \frac{9}{16}

• W' is exactly 9/16 of the surface weight.

Step 3

Calculate Final Weight at Height h

Substitute W₀ = 48 N into the equation:

W' = 48\text{ N} \times \frac{9}{16} = 3 \times 9\text{ N} = 27\text{ N}

• Matches Option (2) perfectly.

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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 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Corresponds to using approximation g' = g(1 - 2h/R) = 48(1 - 2/3) = 16 N, which is completely invalid for large h = R/3.

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Student Fallacy (Why candidates pick this trap): Using small-height binomial approximation g(1 - 2h/R) when h = R/3.

2 B

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. Exact inverse-square law gives W' = 48 × (3/4)² = 27 N.

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Why this is airtight: None; rigorous application of Newton’s law.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Obtained from linear depth formula g(1 - d/R) with d = R/3 (48 × 2/3 = 32 N), confusing altitude with depth!

⚠️

Student Fallacy (Why candidates pick this trap): Applying depth formula instead of altitude formula.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Arbitrary distractor (48 × 3/4).

⚠️

Student Fallacy (Why candidates pick this trap): Forgetting to square the distance ratio (using R/r instead of (R/r)²).

⚠️

NTA Trap Alert: The Binomial Approximation Trap g' ≈ g(1 - 2h/R)

The formula g' = g(1 - 2h/R) is ONLY valid for h << R (e.g. h < 5% of R). Here h = R/3 (33% of R), for which the approximation gives 16 N (Option 1). Using the exact formula gives the true value 27 N!

🛡️ How to avoid the -1 mark: If h is a fraction of R like R/2, R/3, or R, ALWAYS use g' = g / (1 + h/R)².

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Core NEET Syllabus Standard

NEET Physics Core Syllabus · Gravitation Standard Benchmark

Core Scientific Principle Tested:

"g' = g / (1 + h/R)² = GM / (R + h)²."

Syllabus Focus: Acceleration Due to Gravity Above the Earth’s Surface

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Center distance is 4/3 R ⟹ Force scales by (3/4)² = 9/16 ⟹ 48 × 9/16 = 27 N!

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NEET 2025 Physics Question 32 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Inverse-Square Distance Scaling Rule

Step-by-Step Rigorous Workflow & Mathematical Proof

Identify Radial Distance from Center of Earth

Formulate Exact Gravitational Force Equation

Calculate Final Weight at Height h

360° Option Elimination Engine Key Feature

NTA Trap Alert: The Binomial Approximation Trap g' ≈ g(1 - 2h/R)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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