Gravitation and Floating: Class 9 Study Guide
Gravity pulls every object towards every other. Objects float or sink depending on the upward force of the liquid.
Newton's law of gravitation says that every object attracts every other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G m₁m₂ ÷ r². The constant G is 6.67 × 10⁻¹¹ N m²/kg².
Near the Earth's surface, free-falling objects have the acceleration due to gravity, g, about 9.8 m/s². We often use 10 m/s² for easy sums. All objects fall with the same acceleration in a vacuum.
Mass and weight
Mass is the amount of matter in a body, in kg, and does not change from place to place. Weight is the force of gravity on it, W = mg, in newtons. A 60 kg person weighs about 600 N on Earth (using g = 10). On the Moon, g is about one sixth as much, so the weight is about 100 N but the mass is still 60 kg.
| Quantity | Unit | Changes with place? |
|---|---|---|
| Mass | kg | No |
| Weight | N | Yes |
| g | m/s² | Yes, about 9.8 on Earth |
Free fall
A stone dropped from rest falls with v = gt and distance s = ½gt². After 3 s (g = 10), v = 30 m/s and s = 45 m. A feather falls slowly in air because of air resistance, but in a vacuum it falls as fast as a stone.
Dropped from rest.
For speed.
For distance.
m/s and m.
Buoyancy and Archimedes' principle
A liquid pushes up on an object in it with an upward force called buoyancy. Archimedes' principle says the buoyant force equals the weight of the liquid displaced. An object floats if its density is less than the liquid's, and sinks if it is more. Density = mass ÷ volume. Water has a density of 1000 kg/m³, so a ship floats because its overall density is less.
Worked examples and common mistakes
Example: An object has mass 5 kg. Weight = 50 N (g = 10). Example: A 200 g block of volume 100 cm³ has a density of 2 g/cm³, so it sinks in water. Common mistakes: saying mass changes on the Moon, mixing up G and g, and using grams in a formula that needs kilograms.
Check your understanding: model answers
1. 120 N. 2. ½ × 10 × 4 = 20 m. 3. Yes, since 800 is less than 1000.
✨ Key Takeaways
- Gravitation depends on masses and the square of the distance.
- g is about 9.8 m/s² near the Earth.
- Weight = mg, and mass does not change with place.
- Objects float if their density is less than the liquid's.
💬 Questions for Discussion & Reflection
- Find the weight of a 12 kg body (g = 10).
- How far does a stone fall in 2 s from rest (g = 10)?
- Will an object of density 800 kg/m³ float in water?
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