Q1. Calculate the force between two 5 kg and 10 kg masses kept 0.5 m apart. (G = 6.67×10⁻¹¹)
F = G m₁ m₂ / r²
F = 6.67×10⁻¹¹ × 5 × 10 / (0.5)²
F = 6.67×10⁻¹¹ × 50 / 0.25 = 1.33×10⁻⁸ N
Gravitation — Class 9
Why does a dropped pen fall but the Moon doesn't? Same law, different speeds. Compute gravitational force and free fall, and practise the numericals examiners love.
Universal law of gravitationEvery body attracts every other with a force F = G·m₁·m₂/r², directly proportional to the masses and inversely to the square of the distance.
Acceleration due to gravity (g)The acceleration of a freely falling body, g = GM/R² ≈ 9.8 m/s² near Earth. Independent of the falling body's mass.
Mass vs WeightMass (kg) is the amount of matter and is constant. Weight W = m·g (newton) is the gravitational pull and changes with g.
Thrust & PressureThrust is the force acting perpendicular to a surface; pressure P = thrust/area (pascal). Buoyancy is the upward force from a fluid.
Weight & free-fall calculator Interactive
Find weight on Earth and the speed/height of a freely falling body (g = 9.8 m/s²).
Weight, W = m·g—N
Velocity after t, v = g·t—m/s
Height fallen, h = ½g·t²—m
In free fall every object speeds up at the same rate (9.8 m/s²) — a feather and a stone fall together in a vacuum.
Numericals practice Interactive
Free-fall and weight problems with worked steps (take g = 10 m/s²).
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Solved numericals
Q2. A boy weighs 600 N on Earth. What is his mass, and his weight on the Moon (g_moon = g/6)?
m = W/g = 600/10 = 60 kg (mass is unchanged)
Weight on Moon = 600/6 = 100 N
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Gravitational force | F = G m₁ m₂ / r² | N (G = 6.67×10⁻¹¹) |
| Acceleration due to gravity | g = G M / R² | m/s² |
| Weight | W = m g | N |
| Free fall (from rest) | v = g t, h = ½ g t² | m/s, m |
| Pressure | P = F / A | pascal (Pa) |
| Relative density | R.D. = density of substance / density of water | — (no unit) |
Common mistakes & exam wins
- g does not depend on the mass of the falling body — all bodies fall at the same rate.
- Mass stays the same everywhere; only weight changes with g (e.g. 1/6 on the Moon).
- Always square the distance r in the universal law — it's the inverse-SQUARE law.
- Pressure increases if the same force acts on a smaller area (that is why a sharp knife cuts better).
Frequently asked questions
What is the universal law of gravitation?
Every object attracts every other object with a force F = G·m₁·m₂/r², proportional to the product of their masses and inversely proportional to the square of the distance between them.
What is the difference between mass and weight?
Mass (kg) is the amount of matter in a body and is constant. Weight (newton) is the gravitational force on it, W = m·g, and varies with g.
Why does a body weigh less on the Moon?
Because the Moon's gravitational acceleration is about one-sixth of Earth's, so W = m·g is about one-sixth, even though the mass is unchanged.
What is Archimedes' principle?
A body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.