Q.8 Physics · Section A ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 8 Solution

Topic: Gravitation · Official NTA Booklet Code T1

Question

The mass of a planet is 1/10th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

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Verified Against NTA Final Answer Key

Option (2) : 3.92 m s⁻²

📚 Gravitation Easy

📋 Given Parameters & Problem Setup

Planet mass ratio M_p = M_e / 10

Planet diameter ratio D_p = D_e / 2 => R_p = R_e / 2

Earth surface gravity g_e = 9.8 m s⁻²

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The 30-Second Exam Hall Shortcut: ⚡ Proportionality Scaling Hack

⏱️ Save ~40 seconds

g ∝ M / R² -> g_p = g_e × (1/10) / (1/2)² = 9.8 × 4 / 10 = 3.92 m s⁻²!

1 Surface gravity formula: g = GM / R².

2 Mass scales by factor of 1/10.

3 Radius scales by factor of 1/2, so R² scales by (1/2)² = 1/4.

4 Ratio: g_p / g_e = (1/10) / (1/4) = 4 / 10 = 0.4.

5 g_p = 0.4 × 9.8 = 3.92 m s⁻². Pick Option (2) in under 10 seconds!

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Why You Can 100% Trust This Shortcut: Newton’s Law of Universal Gravitation (Surface gravity formula: g = GM/R²).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Governing Formula for Surface Gravity

The acceleration due to gravity on the surface of a spherical celestial body of mass M and radius R is given by Newton’s law of gravitation:

g = \frac{G M}{R^2}

Step 2

Ratio Formation

Writing the ratio of the planet’s surface gravity g_p to Earth’s surface gravity g_e:

\frac{g_p}{g_e} = \left(\frac{M_p}{M_e}\right) \left(\frac{R_e}{R_p}\right)^2

Step 3

Substitution of Scaling Factors

Given that M_p = M_e / 10 and diameter is halved (meaning radius R_p = R_e / 2):

\frac{g_p}{g_e} = \left(\frac{1}{10}\right) \left(\frac{R_e}{R_e / 2}\right)^2 = \frac{1}{10} \times 2^2 = \frac{4}{10} = 0.4

Step 4

Numerical Evaluation

Multiplying by standard Earth surface gravity g_e = 9.8 m s⁻²:

g_p = 0.4 \times 9.8\,\text{m s}^{-2} = 3.92\,\text{m s}^{-2}

⭐

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:

Occurs if radius is not squared in the denominator (9.8 × 2 / 4 = 4.9).

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Student Fallacy (Why candidates pick this trap): Forgetting the square in the denominator: writing g ∝ M/R instead of M/R².

2 (2)

✓ 100% Correct

Verdict & Scientific Reason:

Exact solution: g_p = 0.4 × 9.8 = 3.92 m s⁻².

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Why this is airtight: None.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Twice of Earth gravity; occurs if mass is taken as doubled rather than one-tenth.

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Student Fallacy (Why candidates pick this trap): Inverting the mass and radius ratios.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Standard Earth gravity; ignores the planet’s smaller mass and radius.

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Student Fallacy (Why candidates pick this trap): Assuming planetary gravity is universally constant.

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NTA Trap Alert: Diameter vs Radius Confusion

Students often wonder if the ratio of diameters differs from the ratio of radii.

🛡️ How to avoid the -1 mark: Diameter ratio is identical to radius ratio: D_p/D_e = R_p/R_e. Always replace diameter ratio directly with radius ratio!

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Core NEET Syllabus Standard

Physics Core Mechanics · Gravitation Standard Benchmark

Core Scientific Principle Tested:

"Surface gravity is directly proportional to mass and inversely proportional to the square of the radius (g = GM/R²)."

Syllabus Focus: Acceleration Due to Gravity of the Earth and Planets

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Radius halves -> Gravity quadruples; Mass drops 10x -> Multiply by 0.4 -> 3.92!

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NEET 2024 Physics Question 8 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Proportionality Scaling Hack

Step-by-Step Rigorous Workflow & Mathematical Proof

Governing Formula for Surface Gravity

Ratio Formation

Substitution of Scaling Factors

Numerical Evaluation

360° Option Elimination Engine Key Feature

NTA Trap Alert: Diameter vs Radius Confusion

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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