Gravitation – IIT/JEE Tough Problems
Phase 2 • Page 8 • Extreme Conceptual & Multi-Step Questions
Tough Problem 11: Escape Velocity from Inside Earth
Q: A particle is located at a depth d below Earth’s surface. Find escape velocity from that point.
Solution:
Effective radius:
r = R − d
Mass contributing to gravity:
Mr ∝ r³
Escape velocity inside Earth:
ve = √(GM/R³) × √(3R² − r²)
IIT Insight: Escape velocity decreases inside Earth but never becomes zero.
Tough Problem 12: Two Satellites in Perpendicular Orbits
Q: Two satellites move in circular orbits of same radius but in perpendicular planes. Find their relative velocity when they cross.
Solution:
Orbital speed:
v = √(GM/R)
Relative velocity:
vrel = √(v² + v²) = v√2
Trap: Do NOT subtract speeds. Use vector addition.
Tough Problem 13: Satellite Released from Rest at Height
Q: A satellite is released from rest at height h above Earth. Describe its motion.
Answer:
- Falls radially inward
- No circular motion occurs
- Speed increases continuously
Concept: Circular motion requires tangential velocity.
Tough Problem 14: Minimum Speed for Circular Orbit at Height h
Q: Find minimum speed required to maintain circular orbit at height h.
Solution:
v = √(GM / (R + h))
Exam Trick: Never confuse orbital speed with escape velocity.
Tough Problem 15: Gravitational Force Between Earth & Satellite Inside Tunnel
Q: How does gravitational force vary when satellite is inside a straight tunnel passing through Earth?
Answer:
F ∝ r
Force decreases linearly towards centre and becomes zero at centre.
IIT Favourite: Linear force → SHM motion.
Tough Problem 16: Satellite Speed Change on Lowering Orbit
Q: If satellite orbit radius decreases, what happens to speed?
Answer:
- Speed increases
- Total energy decreases
- Time period decreases
Paradox: Lower energy but higher speed confuses many students.
Elite Gravitation Rule
Always analyze: Radial vs tangential velocity before choosing formulas.
Phase 2 • Page 8 Completed Successfully ✅
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- 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
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- 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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