Gravitation – IIT/JEE Tough Problems
Phase 2 • Page 7 • Rank-Deciding Problems & Hidden Traps
Tough Problem 6: Satellite Transferred Between Two Orbits
Q: A satellite is transferred from a circular orbit of radius R to another circular orbit of radius 4R. Find the ratio of energies supplied at the two transfer points.
Solution:
Initial energy:
E₁ = −GMm / (2R)
Final energy:
E₂ = −GMm / (8R)
Energy supplied:
ΔE = E₂ − E₁ = (3GMm)/(8R)
IIT Insight: Energy is supplied in stages, not continuously.
Tough Problem 7: Gravitational Field Zero Point (Conceptual)
Q: At what point inside Earth is gravitational field intensity maximum?
Answer:
Gravitational field intensity increases linearly from centre to surface. Hence, it is maximum at Earth’s surface.
Trap: Many students think it is maximum at centre—this is wrong.
Tough Problem 8: Satellite Losing Energy Gradually
Q: A satellite loses energy continuously due to drag. Describe how its orbit, speed, and time period change.
Answer:
- Orbit radius decreases
- Orbital speed increases
- Time period decreases
Advanced Thinking: Lower orbit → faster motion but lower energy.
Tough Problem 9: Satellite Moving Along Diameter of Earth
Q: A tunnel is drilled along Earth’s diameter. A particle is released inside it. Describe the motion of the particle.
Solution:
Inside Earth, gravitational force ∝ distance from centre. The particle executes simple harmonic motion with centre at Earth’s centre.
IIT Favourite: This is a classic gravitation + SHM crossover.
Tough Problem 10: Variation of Potential Energy Inside Earth
Q: How does gravitational potential energy vary inside Earth?
Answer:
Inside Earth, gravitational potential energy varies as:
U ∝ −r²
It is minimum at the centre and maximum (least negative) at the surface.
Key Concept: Potential is quadratic inside Earth, not inverse.
Phase-2 Elite Thinking Rule
In tough problems, track sign of energy and trend of radius instead of calculating numbers.
Phase 2 • Page 7 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
- 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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