Gravitation – IIT/JEE Solved Problems

Phase 1 • Page 1 • Basic to Moderate Problems

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Problem 1: Force Between Two Masses

Q: Two bodies of masses 5 kg and 10 kg are placed 2 m apart. Find the gravitational force between them.

Solution:

• m₁ = 5 kg
• m₂ = 10 kg
• r = 2 m
• G = 6.67 × 10⁻¹¹ N m²/kg²

Using Newton’s law:
F = G m₁m₂ / r²

F = (6.67 × 10⁻¹¹ × 5 × 10) / 4
F = 8.34 × 10⁻¹⁰ N

Thinking Tip: Order of magnitude matters more than exact value in IIT screening.

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Problem 2: Acceleration Due to Gravity

Q: Calculate acceleration due to gravity on Earth’s surface. (Given M = 6 × 10²⁴ kg, R = 6.4 × 10⁶ m)

Solution:

g = GM / R²

g = (6.67 × 10⁻¹¹ × 6 × 10²⁴) / (6.4 × 10⁶)²

g ≈ 9.8 m/s²

IIT Insight: Never memorize g blindly—know how it comes from GM/R².

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Problem 3: Weight Change on Moon

Q: A person weighs 600 N on Earth. Find his weight on Moon.

Solution:

g_moon = g/6

Weight on Moon = 600 / 6 = 100 N

Trap Alert: Mass remains same — only weight changes.

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Problem 4: g at Height h

Q: Find g at a height h = R above Earth’s surface.

Solution:

Distance from centre = R + h = 2R

g_h = g (R² / (2R)²) = g/4

Method Tip: Always write distance from centre first.

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Problem 5: Escape Velocity (Conceptual)

Q: Why does escape velocity not depend on mass of the body?

Answer:

Escape velocity is obtained using energy conservation. Mass of the body cancels during derivation, so escape velocity depends only on planet’s mass and radius.

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Phase-1 Solving Method (Must Learn)

• Step 1: Identify distance from centre
• Step 2: Decide required formula
• Step 3: Use proportionality first
• Step 4: Substitute values last

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Phase 1 • Page 1 Completed Successfully ✅