Gravitation – IIT/JEE Solved Problems

Phase 1 • Page 3 • Escape Velocity & Energy Concepts

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Problem 11: Escape Velocity from Earth

Q: Derive the expression for escape velocity of a body from Earth.

Solution:

Escape velocity is obtained using conservation of energy.

• Kinetic energy at surface = ½mv²
• Gravitational potential energy at surface = −GMm/R
• At infinity, total energy = 0

½mv² − GMm/R = 0

v = √(2GM/R)

Core IIT Idea: Escape velocity comes from energy balance, not force equations.

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Problem 12: Escape Velocity on Moon

Q: If escape velocity on Earth is 11.2 km/s, find escape velocity on Moon. (g_moon = g/6, R_moon ≈ R/4)

Solution:

v_e ∝ √(gR)

v_moon/v_earth = √[(g/6 × R/4)/(g × R)]

v_moon = v_earth / √24

Shortcut: Never calculate GM again—use proportionality.

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Problem 13: Energy of Satellite

Q: Find total mechanical energy of a satellite in circular orbit of radius r.

Solution:

Kinetic energy = GMm / (2r)

Potential energy = −GMm / r

Total energy = −GMm / (2r)

IIT Favourite: Negative total energy ⇒ satellite is bound to Earth.

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Problem 14: Effect of Height on Escape Velocity

Q: Does escape velocity depend on height from Earth’s surface?

Answer:

Escape velocity depends on distance from centre of Earth. At a height h, escape velocity becomes:

v = √(2GM / (R + h))

Important: Escape velocity decreases with increase in height.

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Problem 15: Satellite Falling Towards Earth

Q: Why does a satellite not fall straight down to Earth?

Answer:

Satellite has sufficient horizontal velocity. While it falls towards Earth, Earth curves away at the same rate. Thus, satellite remains in orbit.

Concept Insight: Orbit is continuous free fall.

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Phase-1 Master Formula Set

• g = GM/R²
• v = √(GM/r)
• T = 2π √(r³/GM)
• v_e = √(2GM/R)
• E = −GMm / (2r)

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Phase 1 • Page 3 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
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• 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
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• Gravitation – Part 34
• Gravitation – Part 35
• Gravitation – Part 36
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• Gravitation – Part 38
• Gravitation – Part 39
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• Gravitation – Part 41
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