Gravitation – Phase 3 (Objective Mastery)

Page 4B • IIT/JEE Tough Objective Questions (Q26–Q50)

This page increases difficulty by combining gravitation + motion + reasoning. These are typical rank-separator questions.

Q26. Satellite Just Escapes

A satellite is projected vertically upward with escape velocity. Its speed at infinity will be:

Answer: Zero

Concept: Escape velocity defined for zero speed at infinity Trap: Many think it escapes with speed

Q27. Gravitational Field vs Potential

At Earth’s centre:

Gravitational field = 0 ✔
Gravitational potential ≠ 0 ✔

Exam Favourite: Field cancels, potential adds

Q28. Ratio of Escape Velocities

Two planets have same mass but radii R and 4R. Ratio of escape velocities?

Answer: 2 : 1

Method: v_e ∝ 1/√R Shortcut: √(4R) = 2√R

Q29. Satellite Angular Speed Change

If orbital radius decreases, angular speed:

Answer: Increases

Reason: ω ∝ 1/r^3/2

Q30. Zero Work Condition

Gravitational force does zero work when motion is:

Answer: Perpendicular to force (circular orbit)

Key: Force ⟂ displacement

Q31. Energy Sign in Bound Orbit

Total energy of satellite in circular orbit is:

Answer: Negative

Meaning: Bound system

Q32. Satellite Fired Tangentially Faster

Satellite fired with speed greater than orbital speed but less than escape speed. Path followed?

Answer: Elliptical orbit

Insight: Only exact speed → circular

Q33. g Inside Earth

Variation of g with depth is:

Answer: Linear

Memory Hook: Straight line to centre

Q34. Kepler’s Law Check

Which law relates time period and radius?

Answer: Third law

Formula: T² ∝ r³

Q35. Potential Difference Zero When

Potential difference between two points is zero if:

Answer: Both points at same distance from centre

Radial Symmetry Concept

Q36. Mass Change of Satellite

If mass of satellite increases, orbital speed:

Answer: Remains same

Trap: Satellite mass irrelevant

Q37. Geostationary Satellite Plane

Geostationary satellite must be in:

Answer: Equatorial plane

Examiner Check: Concept + fact

Q38. Gravitational Potential Energy Reference

Standard zero of gravitational PE is taken at:

Answer: Infinity

Q39. Two Satellites Same Period

Two satellites have same period. Their orbital radii are:

Answer: Equal

Kepler’s 3rd Law

Q40. Velocity at Apogee

Satellite velocity at apogee is:

Answer: Minimum

Energy Distribution Insight

Q41–Q50 (High-Level Pattern Set)

Impulse direction effect on orbit
Satellite thrown radially inward
Comparing escape & orbital speeds
Field cancellation symmetry problems
Potential vs force conceptual MCQs
Dimension-based gravitation MCQs
Graph-based g vs r questions
Multi-statement assertion–reason
Energy sign interpretation
Examiner designed trick questions

Student Warning: Q26–Q50 decide whether you cross the cutoff.

PAGE 4B FINAL MESSAGE

If these questions feel uncomfortable, you are learning correctly.

Phase 3 • Page 4B (Q26–Q50) Completed ✅

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