PA03 — Gravitation

✈ Physics – PA03 · AFCAT General Awareness AFCAT Level

Gravitation explains why objects fall, how planets orbit, and why astronauts float in space. For AFCAT, focus on the value of g, its variation, the difference between mass and weight, and the key values of escape and orbital velocity — these are direct recall questions.

📌 AFCAT Focus: "What is the value of g on the Moon?" (≈ 1.6 m/s² = g/6), "escape velocity from Earth?" (11.2 km/s), "what is the SI unit of G?" (N m² kg⁻²), "where is g maximum on Earth?" (at the poles). These four facts cover most AFCAT gravitation questions.

1. Newton's Law of Gravitation

Newton's Law of Universal Gravitation:

● F = G × m₁ × m₂ / r²
F = gravitational force; G = 6.67 × 10⁻¹¹ N m² kg⁻² (universal constant)
m₁, m₂ = masses of the two bodies; r = distance between their centres

● G is universal — same everywhere in the universe. It never changes.
● g is local — it varies with location, altitude, and depth.

● Acceleration due to gravity at Earth's surface: g = GM/R² ≈ 9.8 m/s² ≈ 10 m/s²

2. Variation of g

Fig. 1 — How g Changes with Location — A Visual Summary

3. Mass vs Weight

▶ Mass

Amount of matter in a body
Scalar quantity
SI unit: kilogram (kg)
Remains constant everywhere
Measured by: balance (pan balance)
Does NOT depend on gravity

▶ Weight

Gravitational force on a body: W = mg
Vector quantity (acts downward)
SI unit: Newton (N)
Changes with location (depends on g)
Measured by: spring balance
Zero in free fall / space (weightlessness)

4. Escape Velocity & Orbital Velocity

Critical Values to Memorise for AFCAT:

● Escape velocity from Earth = √(2gR) ≈ 11.2 km/s
● Orbital velocity at Earth's surface = √(gR) ≈ 7.9 km/s
● Relation: v_escape = √2 × v_orbital
● Geostationary satellite: Period = 24 hours; Height ≈ 36,000 km; appears stationary
● Astronauts feel weightless because they are in free fall — NOT because gravity is absent

📝 AFCAT PYQs — Gravitation

Q1. The weight of an object on the Moon is approximately what fraction of its weight on Earth? AFCAT PYQ

(a) 1/2(b) 1/4(c) 1/6(d) 1/8

✔ Answer: (c) 1/6

g on Moon ≈ 1.6 m/s² ≈ g_Earth/6. Since W = mg, the weight on Moon = m × (g/6) = Earth weight/6. Mass stays the same. A 60 kg person weighs 600 N on Earth but only 100 N on Moon. This 1/6th fact is directly and repeatedly tested in AFCAT.

Q2. The escape velocity from Earth's surface is approximately: AFCAT PYQ

(a) 7.9 km/s(b) 9.8 km/s(c) 11.2 km/s(d) 3 km/s

✔ Answer: (c) 11.2 km/s

Escape velocity = √(2gR) ≈ 11.2 km/s. This is the minimum speed needed to escape Earth's gravitational pull without any further thrust. Orbital velocity at Earth's surface ≈ 7.9 km/s. Note: escape velocity = √2 × orbital velocity. Both values are directly tested in AFCAT.

Q3. A geostationary satellite appears stationary because it completes one revolution in: AFCAT PYQ

(a) 12 hours(b) 24 hours(c) 6 hours(d) 48 hours

✔ Answer: (b) 24 hours

A geostationary satellite orbits at ~36,000 km altitude with exactly the same time period as Earth's rotation: 24 hours. From Earth it appears stationary. Used for: communication satellites (DTH TV, internet), weather monitoring. Must be positioned over the equator.

🧠 Quick Memory Chart — PA03 Gravitation

🌎 g Values

Earth surface: 9.8 m/s²
Moon: 1.6 m/s² (= g/6)
Earth centre: 0
Poles: highest; Equator: lowest
G = 6.67×10⁻¹¹ N m² kg⁻²

🚀 Velocities

Escape: 11.2 km/s
Orbital: 7.9 km/s
v_esc = √2 × v_orb
Geostationary: 24h, 36,000 km
Weightlessness = free fall

⚖ Mass vs Weight

Mass: kg, scalar, constant
Weight: Newton, vector, varies
W = mg (always)
Pan balance → mass
Spring balance → weight

📝 Practice Exercise

E1. Where is the value of g maximum on Earth?

(a) At equator(b) At poles(c) At centre(d) At 45° latitude

E2. If mass of a body is 60 kg on Earth, its mass on Moon is:

(a) 10 kg(b) 6 kg(c) 60 kg(d) 360 kg

E3. The orbital velocity of a satellite near Earth's surface is approximately:

(a) 11.2 km/s(b) 7.9 km/s(c) 3 km/s(d) 9.8 km/s

Answers: E1 → (b) Poles [Earth is flatter at poles — closer to centre + no centrifugal effect] | E2 → (c) 60 kg [Mass never changes; only weight changes] | E3 → (b) 7.9 km/s

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