Gravity and Variation in g
~9 min read
- Universal law: F = G·m₁m₂/r². G = 6.67 × 10⁻¹¹ N·m²/kg².
- Value of g: g = 9.8 m/s² (Earth surface average). Decreases with altitude, depth, and from poles to equator.
- Escape velocity: 11.2 km/s from Earth's surface. Independent of mass of escaping object.
Gravity holds the universe together, from apple to Andromeda. CDS/OTA tests Newton's law of gravitation, value of g and its variation, escape velocity, and satellites.
Universal Law of Gravitation
- F = G·m₁m₂/r² — Newton (1687).
- G = 6.67 × 10⁻¹¹ N·m²/kg² — universal gravitational constant, measured by Henry Cavendish (1798).
- Gravity is always attractive, acts over infinite range, and is the weakest of the four fundamental forces.
- For a body of mass m on Earth's surface: F = mg, so g = GM/R².
Variation in g
| Factor | Effect on g |
|---|---|
| Altitude h above surface | Decreases as g' = g·(R/(R+h))² — top of mountain |
| Depth d below surface | Decreases as g' = g·(1 - d/R) — at centre, g = 0 |
| Latitude | Maximum at poles (9.832 m/s²), minimum at equator (9.780 m/s²) due to Earth's rotation and equatorial bulge |
| Shape of Earth | Oblate spheroid — radius smaller at poles, so g larger there |
Standard value: g = 9.8 m/s² (often taken as 10 m/s² in numericals).
Escape Velocity and Satellites
- Escape velocity v_e = √(2gR) = √(2GM/R).
- For Earth, v_e ≈ 11.2 km/s. For Moon, ~2.4 km/s. For Sun, ~617 km/s.
- Independent of the escaping object's mass.
- Orbital velocity just above surface: v_o = √(gR) ≈ 7.9 km/s. Escape velocity = √2 × orbital velocity.
- Geostationary satellite: period 24 hours; altitude ~36,000 km; orbits over equator; appears stationary.
Mass vs Weight
- Mass — amount of matter (kg, scalar, constant).
- Weight — gravitational force on the body, W = mg (newton, vector).
- On Moon, g_moon ≈ g/6, so weight is one-sixth that on Earth, but mass is unchanged.
- In free fall or in orbit, apparent weight = 0 (weightlessness), though gravity still acts.
CDS/OTA PYQ Examples
Q: Escape velocity from Earth's surface is approximately:
(a) 7.9 km/s (b) 9.8 km/s (c) 11.2 km/s (d) 22 km/s
Answer: (c) 11.2 km/s.
Q: Value of g is maximum at:
(a) Equator (b) Poles (c) 45° latitude (d) Mountain top
Answer: (b) Poles — Earth's radius smaller and no centrifugal effect.
Q: At the centre of the Earth, weight of an object is:
(a) Same as on surface (b) Half (c) Double (d) Zero
Answer: (d) Zero — g = 0 at centre.
Q: Universal gravitational constant G was measured by:
(a) Newton (b) Galileo (c) Cavendish (d) Einstein
Answer: (c) Henry Cavendish (1798) — torsion balance experiment.
Q: A geostationary satellite has a period of:
(a) 1 hour (b) 12 hours (c) 24 hours (d) 48 hours
Answer: (c) 24 hours, matching Earth's rotation.
Drill Gravity and Variation in g for CDS/OTA
CDS/OTA-pattern items on Gravity and Variation in g with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why do astronauts feel weightless in orbit?
They are in continuous free fall around the Earth. Their acceleration equals g at that altitude, so the apparent weight is zero — though gravity is still pulling them.
Is g the same everywhere on Earth?
No. It varies with latitude (max at poles, min at equator), altitude (decreases upward), depth (decreases inward), and local geology.
Why does a feather and a coin fall at the same rate in vacuum?
Because g is independent of mass. In air, the feather is slowed by air resistance; in vacuum (Apollo 15 demonstration on Moon) they fall together.