Gravitation for NEET UG
One law, F = Gm₁m₂/r², explains falling apples, the Moon's orbit and satellites. This chapter shows how.
PhysicsClass 1168 MCQs3 lessons12 flashcards4 memory tricks
What you'll learn
- Newton's law of gravitation and g
Use the law of gravitation and explain how g changes with height and depth. - Gravitational potential energy and escape speed
Calculate potential energy far from the Earth and find escape speed. - Satellites and Kepler's laws
Find orbital speed and period, and apply Kepler's laws.
Key formulas
| Universal law | F = G m₁m₂ / r², G = 6.67 × 10⁻¹¹ N m² kg⁻² |
|---|---|
| g at the surface | g = GM/R² |
| g at height h (h ≪ R) | g_h ≈ g(1 − 2h/R) |
| g at depth d | g_d = g(1 − d/R) |
| Potential energy | U = −GMm/r |
| Escape speed | vₑ = √(2GM/R) = √(2gR) ≈ 11.2 km/s for Earth |
| Orbital speed | v₀ = √(GM/r) |
| Period | T = 2πr/v₀ = 2π√(r³/GM) |
Memory tricks
v = √(GM/r): the satellite's own mass cancels out. Only the planet's mass M and the orbit radius r matter.
Going up: g' ≈ g(1 − 2h/R) for small h. Going down: g' = g(1 − d/R), and g = 0 at the centre. g is greatest at the surface.
Near the surface, escape speed √(2gR) ≈ 11.2 km/s is √2 times the orbital speed √(gR) ≈ 7.9 km/s.
T² ∝ r³. Double the orbit radius and the period becomes 2√2 ≈ 2.8 times longer.
Try 3 NEET-style questions
Q1. If a body is taken from the Earth's surface to a height h (h ≪ R), its gain in gravitational potential energy is approximately
- −mgh
- mgh
- GMm/h
- zero
Show answer
Answer: (2) mgh
For small heights, ΔU = mgh, which comes from the exact expression −GMm/r with h ≪ R.
Q2. A planet orbits the Sun at a mean distance of 4 AU. Its period of revolution is
- 4 years
- 16 years
- 64 years
- 8 years
Show answer
Answer: (4) 8 years
By Kepler's third law T² ∝ r³. T = (4)^(3/2) = 8 years.
Q3. The SI unit of gravitational field strength is
- N/kg
- N kg
- kg/N
- N/m
Show answer
Answer: (1) N/kg
Gravitational field strength is force per unit mass, so its unit is N/kg, which is the same as m/s².
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