Gravitation – Phase 3 (Elite Objective Mastery)
Page 4C • IIT/JEE Tough Objective Questions (Q51–Q75)
This page contains elite-level questions that combine gravitation with logic, graphs, limits, and examiner psychology. These are rank-differentiators.
Q51. Escape Velocity & Mass Loss
A body is projected with escape velocity from Earth. If Earth suddenly loses half its mass, the body will:
Answer: Escape with finite velocity
Method: Total energy becomes positive Trick: ve depends on planet mass
Q52. Field Inside Hollow Sphere
Gravitational field inside a hollow spherical shell is:
Answer: Zero everywhere
Gauss-type symmetry result
Q53. Potential Inside Hollow Sphere
Gravitational potential inside hollow sphere is:
Answer: Constant (non-zero)
Trap: Field zero ≠ potential zero
Q54. Minimum Speed to Just Escape Orbit
Satellite moving in circular orbit. Minimum speed increase required to escape?
Answer: √2 − 1 times orbital speed
Method: Compare orbital & escape velocities IIT Favourite Result
Q55. Work Done from r₁ to r₂
Work done by gravity when particle moves from r₁ to r₂:
Answer: GMm(1/r₂ − 1/r₁)
Conservative force formula
Q56. Satellite Thrown Radially Inward
A satellite is thrown radially inward from circular orbit. Path followed?
Answer: Elliptical (degenerate)
Insight: Angular momentum decreases
Q57. g at Height & Depth Equality
At what depth and height does g become same?
Answer: d = h = R/2 (approx)
Method: Equate g(h) and g(d)
Q58. Satellite Period Change on Radius Change
If orbital radius doubles, time period becomes:
Answer: 2√2 times
Kepler’s law direct use
Q59. Potential Gradient Meaning
Negative gradient of potential represents:
Answer: Gravitational field
Vector insight
Q60. Satellite Thrown Opposite Direction
Velocity of satellite reduced slightly. Orbit becomes:
Answer: Elliptical with perigee at point of impulse
Direction-based trap
Q61. Zero Gravity Region
Between Earth and Moon, g = 0 point is:
Answer: Closer to Moon
Because Earth is heavier
Q62. Escape Velocity from Centre of Earth
Escape velocity from Earth’s centre is:
Answer: Greater than surface escape velocity
More work required
Q63. Gravitational Binding Energy
Binding energy of Earth is proportional to:
Answer: GM²/R
Structure stability concept
Q64. Satellite KE Change
If satellite moves from apogee to perigee, KE:
Answer: Increases
Q65. Gravitational Field Graph
Correct g vs r graph for Earth:
Answer: Linear increase inside, inverse square outside
Classic graph-based MCQ
Q66–Q75 (Ultra-Tricky Patterns)
- Satellite thrust cut-off problems
- Energy sign flip questions
- Field cancellation symmetry traps
- Potential difference zero cases
- Escape velocity from varying radius
- Graph interpretation MCQs
- Multi-statement assertion reasoning
- Dimension elimination problems
- Limit-based gravitation questions
- Hidden rotation + gravitation combos
Reality Check: If you solve these, you are already thinking like an IITian.
PAGE 4C FINAL TAKEAWAY
Discomfort means growth. These questions separate rankers from readers.
Phase 3 • Page 4C (Q51–Q75) Completed ✅
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