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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