Gravitation – IIT/JEE Tough Problems
Phase 2 • Page 6 • Advanced Reasoning & Multi-Concept Questions
Tough Problem 1: Zero Gravity Point
Q: Two planets of masses M and 9M are separated by distance d. Find the point where net gravitational force on a body becomes zero.
Solution:
Let x be distance from mass M.
Force due to M = GMm / x²
Force due to 9M = G(9M)m / (d − x)²
At neutral point:
GM / x² = 9GM / (d − x)²
(d − x)² = 9x²
d − x = 3x
x = d/4
IIT Insight: Neutral point lies closer to smaller mass.
Tough Problem 2: Energy Needed to Shift Orbit
Q: A satellite is moved from orbit of radius R to 3R. Find the energy supplied.
Solution:
Total energy:
E = −GMm / (2r)
Initial energy:
E₁ = −GMm / (2R)
Final energy:
E₂ = −GMm / (6R)
Energy supplied:
ΔE = E₂ − E₁ = GMm / (3R)
Concept: Higher orbit → energy becomes less negative.
Tough Problem 3: Satellite Speed Change
Q: A satellite loses 10% of its kinetic energy due to drag. What happens to its orbital radius?
Solution:
Kinetic energy:
K = GMm / (2r)
Loss of K ⇒ total energy decreases ⇒ r decreases.
So satellite shifts to a lower orbit with higher speed.
IIT Trap: Energy ↓ does NOT mean speed ↓.
Tough Problem 4: Escape Velocity from Height
Q: A particle is projected upward from height h with escape velocity corresponding to that height. What is its speed at infinity?
Answer:
Speed at infinity = zero
Definition Reminder: Escape velocity is minimum velocity to just reach infinity.
Tough Problem 5: Satellite Inside Earth (Conceptual)
Q: Can a satellite orbit inside Earth assuming Earth has a tunnel?
Answer:
Inside Earth, gravitational force decreases linearly with distance. A satellite cannot maintain circular orbit inside Earth. Instead, it executes oscillatory motion.
Advanced Insight: Force inside Earth ∝ r, not 1/r².
Phase-2 Thinking Rule
In tough problems, do NOT jump to formulas. First ask: What happens to energy, radius, speed?
Phase 2 • Page 6 Completed Successfully ✅
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- Gravitation – Part 2
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- Gravitation – Part 7
- Gravitation – Part 8
- Gravitation – Part 9
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- 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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