Gravitation – IIT/JEE Advanced Rank Booster Problems

Phase 2 • Page 10 • High-Frequency Previous Paper Concepts

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Problem 23: Variation of g with Depth & Height (Combined)

Q: At what depth below Earth’s surface and at what height above surface does acceleration due to gravity become half of its surface value?

Solution:

• Below surface: g_d = g (1 − d/R)
• Above surface: g_h = g (R² / (R + h)²)

Half g condition:

• d = R/2
• h = (√2 − 1)R

Exam Trick: Depth → linear relation Height → inverse square relation

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Problem 24: Satellite Orbit Change Due to Impulse

Q: A satellite moving in circular orbit receives a small tangential impulse. What is new orbit?

Answer:

• Orbit becomes elliptical
• Point of impulse becomes perigee or apogee
• Angular momentum conserved

IIT Insight: Any sudden velocity change → ellipse.

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Problem 25: Energy of Satellite at Different Points

Q: Compare total energy of satellite at perigee and apogee.

Answer:

Total energy remains constant throughout orbit.

Trap: Speed changes, but total energy does NOT.

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Problem 26: Escape Velocity from Height h

Q: Find escape velocity of a particle from height h above Earth.

Formula:

v_e = √(2GM / (R + h))

Common Mistake: Using surface escape velocity blindly.

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Problem 27: Geostationary Satellite Conditions

Q: Write conditions for a satellite to appear stationary from Earth.

• Orbital period = 24 hours
• Orbit in equatorial plane
• Direction same as Earth’s rotation

Examiner Love: Conceptual + factual clarity.

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Problem 28: Two Satellites at Different Radii

Q: Compare angular velocities of two satellites at radii r₁ and r₂.

ω ∝ 1 / r^3/2

Shortcut: Larger orbit → slower angular speed.

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MASTER FORMULA BLOCK (Must Remember)

• v_orbit = √(GM/r)
• E = − GMm / (2r)
• T² ∝ r³ (Kepler’s Law)
• v_escape = √(2GM/r)

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EXAM STRATEGY FOR GRAVITATION

If problem involves orbit → use energy & angular momentum
If problem involves fall → use force & acceleration
Never mix both blindly

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Phase 2 • Page 10 Completed Successfully ✅

📚 IIT JEE PHYSICS – COMPLETE MASTER LIBRARY

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🌍 GRAVITATION – IIT JEE EXAM MASTERY (FULL SERIES)

Concept → Board → IIT → Tough → Mastery

• Gravitation – Part 1
• Gravitation – Part 2
• Gravitation – Part 3
• Gravitation – Part 4
• Gravitation – Part 5
• Gravitation – Part 6
• Gravitation – Part 7
• Gravitation – Part 8
• Gravitation – Part 9
• Gravitation – Part 10
• Gravitation – Part 11
• Gravitation – Part 12
• Gravitation – Part 13
• Gravitation – Part 14
• Gravitation – Part 15
• Gravitation – Part 16
• Gravitation – Part 17
• Gravitation – Part 18
• Gravitation – Part 19
• Gravitation – Part 20
• Gravitation – Part 21
• Gravitation – Part 22
• Gravitation – Part 23
• Gravitation – Part 24
• Gravitation – Part 25
• Gravitation – Part 26
• Gravitation – Part 27
• Gravitation – Part 28
• Gravitation – Part 29
• Gravitation – Part 30
• Gravitation – Part 31
• Gravitation – Part 32
• Gravitation – Part 34
• Gravitation – Part 35
• Gravitation – Part 36
• Gravitation – Part 37
• Gravitation – Part 38
• Gravitation – Part 39
• Gravitation – Part 40
• Gravitation – Part 41
• Gravitation – Part 42

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• Momentum & Collisions – Complete Library
• Centre of Mass & System of Particles – Complete Library
• Work, Energy & Power – Complete Library

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• Physics Thinking – How IIT Toppers Think
• Units & Measurements – Intermediate Notes

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