Physics · Class 9-10 · CBSE

Gravitation, Free Fall and Weightlessness

Master Newton’s Universal Law of Gravitation, acceleration due to gravity (g vs G), equations of motion under free fall, mass vs weight, and Archimedes principle.

1Universal Law of Gravitation and Gravity

Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This isNewton’s Universal Law of Gravitation.

Universal Gravitational Force

F=GM⋅mr2F = G \frac{M \cdot m}{r^2}
  • F = Gravitational attractive force in Newtons (N)
  • G = Universal Gravitational Constant = 6.674 × 10⁻¹¹ N·m²/kg²
  • M, m = Masses of the two bodies in kilograms (kg)
  • r = Separation distance between their centres in metres (m)

Critical Distinction: Mass vs Weight

  • Definition

    Mass (m)
    Quantity of matter contained inside a body
    Weight (W)
    Gravitational force pulling a body towards Earth centre

  • Nature

    Mass (m)
    Scalar quantity (only magnitude)
    Weight (W)
    Vector quantity (magnitude + downwards direction)

  • SI Unit

    Mass (m)
    Kilogram (kg)
    Weight (W)
    Newton (N) or kg·m/s²

  • Formula

    Mass (m)
    Constant invariant property: m
    Weight (W)
    W = m × g

  • Variation with Location

    Mass (m)
    Constant everywhere in the universe (Earth, Moon, deep space)
    Weight (W)
    Varies with local acceleration due to gravity (g)

  • Zero value possible?

    Mass (m)
    Never zero for any physical object
    Weight (W)
    Zero at the Earth centre or in free fall (weightlessness)

2Acceleration Due to Gravity (g) and Free Fall

When an object falls towards Earth under the sole influence of gravitational force, it is inFree Fall. The acceleration experienced by a freely falling object is independent of the mass of the body.

Surface Gravitational Acceleration

g=G⋅MERE2≈9.8 m/s2g = \frac{G \cdot M_E}{R_E^2} \approx 9.8\text{ m/s}^2

Free Fall Kinematics Rule Transformations

  1. 1

    1. Replace standard linear acceleration a with +g for falling down: v = u + gt

  2. 2

    2. Height equation replacing horizontal distance s with h: h = ut + (1/2)gt²

  3. 3

    3. Velocity-displacement relation under gravity: v² = u² + 2gh

  4. 4

    4. When an object is thrown upwards, acceleration is opposite: a = -g (so v = u - gt and h = ut - (1/2)gt²)

Real-life example · Solved Board Problem: Stone Dropped from a Tower

A stone is dropped from the top of a 45 m high cliff with initial velocity u =
0. Take g = 10 m/s².
• Time to hit ground: h = ut + (1/2)gt² ⇒ 45 = 0 + (1/2)(10)t² ⇒ 5t² = 45 ⇒ t² = 9 ⇒ t = 3 seconds.
• Striking velocity: v = u + gt = 0 + (10)(3) = 30 m/s.

3Thrust, Pressure and Archimedes Principle

The net perpendicular force acting on a surface is calledThrust, and thrust per unit area is calledPressure(P = F / A, SI unit Pascal = N/m²).

Archimedes Principle and Flotation Rules

  • Density of Body < Liquid Density

    Forces Comparison
    Buoyant Force > Weight of Body
    Observed State
    Floats with a fraction submerged

  • Density of Body = Liquid Density

    Forces Comparison
    Buoyant Force = Weight of Body
    Observed State
    Floats fully submerged at any depth

  • Density of Body > Liquid Density

    Forces Comparison
    Weight of Body > Buoyant Force
    Observed State
    Sinks to the bottom of the container

4Exam Corner: Tips, Mistakes & Board Questions

High-Yield Revision Points

  • The value of g is greater at the poles (9.83 m/s²) and lesser at the equator (9.78 m/s²) because Earth is flattened at poles (R_equator > R_pole).
  • Weight of an object on the Moon is 1/6th of its weight on Earth because g_moon = g_earth / 6.
  • G is a universal constant with unit N·m²/kg², whereas g is a local vector acceleration with unit m/s².
Common mistake: Do not confuse G with g! G never changes anywhere in the cosmos. g depends on the mass and radius of the planet you are standing on.

Exam question · CBSE Class 9/10 Board

An astronaut has a mass of 60 kg on Earth. What will be his mass and weight on the Moon? (g_earth = 9.8 m/s²)
  1. A.Mass =10kg,Weight =98N\text{Mass}\ = 10 kg, \text{Weight}\ = 98 N
  2. B.Mass =60kg,Weight =98N\text{Mass}\ = 60 kg, \text{Weight}\ = 98 N
  3. C.Mass =60kg,Weight =588N\text{Mass}\ = 60 kg, \text{Weight}\ = 588 N
  4. D.Mass =10kg,Weight =588N\text{Mass}\ = 10 kg, \text{Weight}\ = 588 N

Remember

  • Universal gravitation law: ==F = G(M·m)/r²== acts between any two masses.
  • Mass is invariant (constant); weight depends on local gravity: ==W = mg==.
  • Free fall acceleration ==g = 9.8 m/s²== is independent of the falling mass.
  • An object feels weightless during free fall because normal contact reaction drops to zero.

Check yourself

  1. Question 1

    If the distance between two bodies is doubled, the gravitational force between them becomes:

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