Understanding Weight

Discover the difference between mass and weight, and explore how gravity affects weight on Earth and the Moon!

🌍 Earth
10 kg
W = 98 N
Weight = 98 N
🌙 Moon
10 kg
W = 16.3 N
Weight = 16.3 N
Newton's Second Law
F = m × a
Any force acting on an object equals the product of its mass and acceleration. This is the fundamental relationship in mechanics.
Gravitational Force as Weight
W = m × g
Weight is the gravitational force acting on an object. Since this force causes acceleration 'g', we substitute 'a' with 'g' in Newton's second law.
Universal Law of Gravitation
F = G × (M × m) / R²
The gravitational force between two objects depends on their masses (M and m) and the square of the distance (R) between their centers.
Weight on a Planet
W = G × (M × m) / R²
For an object on a planet's surface, the weight equals the gravitational force between the object and the planet.
Deriving g
g = G × M / R²
Comparing W = mg and W = GMm/R², we get g = GM/R². This shows that 'g' depends only on the planet's mass and radius, not on the object's mass.
Mass
⚖️
  • Definition: Amount of matter
  • Unit: Kilogram (kg)
  • Nature: Scalar quantity
  • Variation: Constant everywhere
  • Measurement: Physical balance
Weight
⬇️
  • Definition: Gravitational force
  • Unit: Newton (N)
  • Nature: Vector quantity
  • Variation: Changes with location
  • Measurement: Spring balance
Example 9.4 (NCERT)

Problem: Mass of an object is 10 kg. What is its weight on Earth?

Given:
Mass, m = 10 kg
Acceleration due to gravity, g = 9.8 m/s²
Formula:
W = m × g
Calculation:
W = 10 kg × 9.8 m/s²
W = 98 N
The weight of the object on Earth is 98 N
Example 9.5 (NCERT)

Problem: An object weighs 10 N on Earth. What would be its weight on the Moon?

Given:
Weight on Earth, We = 10 N
Weight on Moon = (1/6) × Weight on Earth
Calculation:
Wm = We / 6
Wm = 10 N / 6
Wm = 1.67 N
The weight of the object on Moon is 1.67 N
🌍 Earth
10 kg
W = 98 N
Weight = 98 N
🌙 Moon
10 kg
W = 16.3 N (1/6)
Weight = 16.3 N
(1/6 of Earth)
Wmoon / Wearth = 1/6

Weight on Moon is 1/6th of weight on Earth

Explore Weight on Different Celestial Bodies
W = m × g
Weight is the force with which Earth (or any celestial body) attracts an object.
SI Unit: Newton (N) - same as force
Nature: Vector quantity (acts vertically downward)
Key Point: Weight varies with location, but mass remains constant

🧮 Interactive Weight Calculator

Enter a mass value and select location to calculate weight

Table 9.1: Celestial Body Data

Celestial Body Mass (kg) Radius (m) g (m/s²)
Earth 5.98 × 10²⁴ 6.37 × 10⁶ 9.8
Moon 7.36 × 10²² 1.74 × 10⁶ 1.63
Key Insights from NCERT

1. Weight Definition: Weight is the force with which Earth attracts every object.

2. Location Dependence: Weight depends on location because 'g' varies with the celestial body.

3. Mass Constancy: Mass remains the same everywhere - on Earth, Moon, or any planet.

4. Proportionality: At a given place, weight is directly proportional to mass (W ∝ m).

5. Moon Relationship: Weight on Moon = (1/6) × Weight on Earth