Gravitation – IIT/JEE Advanced Problems
Phase 2 • Page 9 • Previous Paper Multi-Concept Questions
Advanced Problem 17: Satellite + Spring System
Q: A satellite of mass m is attached to a light spring (k) inside a circular orbit. Find change in orbital radius.
Solution Outline:
- Gravitational force provides centripetal force
- Spring force modifies effective centripetal force
- Use force balance, not energy directly
IIT Tip: Never mix SHM equations blindly with orbital motion.
Advanced Problem 18: Gravitational Field at Centre of Ring + Point Mass
Q: A ring of mass M and radius R lies in a plane. A particle of mass m is placed at centre. Find net gravitational force.
Answer:
Force due to ring = 0 Net force = force due to external mass only
Concept Test: Symmetry kills force but not potential.
Advanced Problem 19: Satellite Losing Energy Gradually
Q: A satellite loses energy due to atmospheric drag. What happens to its angular velocity?
Solution:
- Orbital radius decreases
- Speed increases
- Angular velocity increases sharply
IIT Favourite: Lower orbit → faster satellite.
Advanced Problem 20: Escape Velocity from Another Planet
Q: Planet has same density as Earth but radius = 2R. Find escape velocity.
Solution:
Mass ∝ R³ ve ∝ R
ve,new = 2 ve,Earth
Shortcut: Density constant → escape velocity ∝ radius.
Advanced Problem 21: Satellite Thrown Horizontally from Height
Q: A body is projected horizontally from height h with speed v. Under what condition will it orbit Earth?
Answer:
v = √(GM / (R + h))
Deep Insight: Orbit is continuous free fall.
Advanced Problem 22: Moon Falling Towards Earth?
Q: Why does Moon not fall into Earth?
Answer:
- Moon is continuously falling
- But tangential velocity keeps missing Earth
- Perfect balance of gravity & inertia
Conceptual Gold: Orbit = sideways fall.
Examiner’s Hidden Test
Examiner checks whether student understands motion, not memorization.
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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
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- 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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