📑 Topics on this page (Jump to Topic):
📌 1. Law of Gravitation & g
- F = G m₁m₂ / r²; G = 6.67 × 10⁻¹¹ N·m²/kg² — a universal constant (same everywhere).
- Doubling the distance makes the force 1/4 (inverse-square law).
- On Earth g ≈ 9.8 m/s²; on the Moon g is about 1/6 of Earth's.
- g is maximum at the poles and minimum at the equator; it decreases with both height and depth; at the Earth's centre g = 0.
- If the Earth spun faster, g at the equator would decrease (poles unaffected).
| Mass | Weight | |
|---|---|---|
| Definition | Quantity of matter | Force of gravity W = mg |
| Type | Scalar | Vector |
| Unit | kg | newton (N) |
| On the Moon | Remains the same | Becomes 1/6 |
| Measured by | Beam balance | Spring balance |
📌 2. Weight in a Lift & Weightlessness
| Lift condition | Apparent weight |
|---|---|
| At rest or uniform velocity | Normal (mg) |
| Accelerating up | More, m(g+a) |
| Accelerating down | Less, m(g−a) |
| Cable breaks — free fall | Zero (weightlessness) |
- Astronauts in orbit feel weightless because they and the craft are in continuous free fall — gravity is not zero.
📌 3. Escape Velocity, Satellites & Kepler
- Earth's escape velocity ≈ 11.2 km/s; the Moon's ≈ 2.4 km/s (so the Moon has no atmosphere).
- Orbital velocity near Earth ≈ 7.9 km/s; escape velocity = √2 × orbital velocity. Escape velocity does not depend on the body's mass.
- Geostationary satellite: height ≈ 35,786 km, period 24 hours, above the equator moving west to east — communication and weather satellites (INSAT/GSAT).
- Polar/sun-synchronous satellites pass over the poles in low orbit — remote sensing and mapping (launched by PSLV).
- Kepler's laws: (1) planets move in elliptical orbits with the Sun at one focus; (2) areal velocity is constant — faster near the Sun; (3) T² ∝ r³.
⚠️ Exam Traps:
- Weightlessness does not mean zero gravity.
- Going higher reduces weight, not mass.
- A satellite's period depends on its orbit radius, not its mass.
📌 4. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. The escape velocity of the Earth is about: Practice
Correct answer: (C)
Minimum speed to escape Earth for ever ≈ 11.2 km/s.
Minimum speed to escape Earth for ever ≈ 11.2 km/s.
Q2. Where is the value of g maximum on the Earth's surface? Practice
Correct answer: (B)
At the poles the radius is smaller and there is no rotational effect, so g is maximum.
At the poles the radius is smaller and there is no rotational effect, so g is maximum.
Q3. The weight of a body on the Moon compared to the Earth is: Practice
Correct answer: (C)
On the Moon g ≈ 1/6 of Earth's; mass stays the same.
On the Moon g ≈ 1/6 of Earth's; mass stays the same.
Q4. The value of g at the centre of the Earth is: Practice
Correct answer: (C)
g decreases with depth and is zero at the centre.
g decreases with depth and is zero at the centre.
Q5. If the distance between two bodies is doubled, the gravitational force becomes: Practice
Correct answer: (B)
F ∝ 1/r²; (1/2)² = 1/4.
F ∝ 1/r²; (1/2)² = 1/4.
Q6. The apparent weight of a person in a freely falling lift is: Practice
Correct answer: (C)
g − a = 0 when a = g.
g − a = 0 when a = g.
Q7. The period of a geostationary satellite is: Practice
Correct answer: (A)
Matching Earth's rotation, it appears fixed in the sky.
Matching Earth's rotation, it appears fixed in the sky.
Q8. A geostationary satellite orbits at about what height above the Earth? Practice
Correct answer: (B)
About 36,000 km; 3,84,000 km is the Moon's distance.
About 36,000 km; 3,84,000 km is the Moon's distance.
Q9. The correct statement about mass: Practice
Correct answer: (D)
Mass is the quantity of matter; weight (mg) changes with place.
Mass is the quantity of matter; weight (mg) changes with place.
Q10. The value of the gravitational constant G is: Practice
Correct answer: (B)
G is universal; g depends on location.
G is universal; g depends on location.
Q11. Why do astronauts feel weightless in orbit? Practice
Correct answer: (D)
g is still large there; weightlessness is due to free fall.
g is still large there; weightlessness is due to free fall.
Q12. The main reason the Moon has no atmosphere: Practice
Correct answer: (D)
Gas molecules can exceed the Moon's low escape velocity (≈2.4 km/s).
Gas molecules can exceed the Moon's low escape velocity (≈2.4 km/s).
Q13. According to Kepler, planetary orbits are: Practice
Correct answer: (B)
The Sun is at one focus of the ellipse — Kepler's first law.
The Sun is at one focus of the ellipse — Kepler's first law.
Q14. When a planet is nearest the Sun, it moves: Practice
Correct answer: (A)
Areal velocity is constant (Kepler's second law) — nearer means faster.
Areal velocity is constant (Kepler's second law) — nearer means faster.
Q15. In a lift accelerating upward, a person's weight appears: Practice
Correct answer: (C)
Apparent weight = m(g + a).
Apparent weight = m(g + a).
Q16. The instrument to measure weight is: Practice
Correct answer: (A)
A spring balance measures force (weight); a beam balance compares mass.
A spring balance measures force (weight); a beam balance compares mass.
Q17. How does escape velocity depend on the mass of the body thrown? Practice
Correct answer: (D)
vₑ = √(2GM/R); it depends on the planet's mass and radius.
vₑ = √(2GM/R); it depends on the planet's mass and radius.
Q18. Which satellites are usually used for remote sensing and mapping? Practice
Correct answer: (A)
From low orbit they repeatedly scan the whole Earth.
From low orbit they repeatedly scan the whole Earth.
Q19. Orbital velocity of a satellite close to the Earth is about: Practice
Correct answer: (A)
vₒ ≈ 7.9 km/s; vₑ = √2 × vₒ ≈ 11.2 km/s.
vₒ ≈ 7.9 km/s; vₑ = √2 × vₒ ≈ 11.2 km/s.
Q20. The weight of a body at a mountain top is: Practice
Correct answer: (D)
g decreases with height, so weight decreases.
g decreases with height, so weight decreases.