Centripetal Force

• Force acting towards the centre of circular path.

• Example: Moon revolves around Earth due to Earth’s centripetal force.

Newton’s Observations

• Apple falls because Earth attracts it.

• Apple also attracts Earth (Newton’s 3rd law).

• Conclusion: All objects attract each other → Gravitational Force.

Universal Law of Gravitation

Formula:

• 

• Explains: planetary motion, tides, etc.

Acceleration Due to Gravity (g)

Formula:

• 

• Greater at poles, less at equator.

Free Fall

Equations of motion under gravity (replace a with g):

Cases:

1. Object dropped from rest (u=0):

2. Object thrown downwards (u ≠ 0):

3. Object thrown upwards (g negative):

Mass vs Weight

Mass (m)	Weight (W = mg)
Quantity of matter	Force due to gravity
Scalar	Vector
Constant everywhere	Changes with location (g)
SI unit: kg	SI unit: N
Never zero	Zero where no gravity (e.g., space)

Weight on Moon

Thrust and Pressure

• Thrust: Force acting perpendicular to a surface.

• Pressure: Force per unit area.

• SI unit: Pascal (Pa)

💡 Nails are sharp → small area → large pressure.

Buoyancy

• Liquids exert upward force = Buoyant Force.

• Float if Buoyant Force > Weight, sink if opposite.

Archimedes’ Principle

Statement:
When a body is immersed in a fluid, it experiences an upward force = weight of fluid displaced.

Applications:

• Ships & submarines

• Lactometer, Hydrometer

• Relative density measurement

Density & Relative Density

• Density:
  

• Relative Density (RD):
  

• No unit (ratio).

💡 RD < 1 → Object floats. RD > 1 → Object sinks.

---

📝 Must-Remember Formulas

1. 

2. 

3. 

4. 

5. 

6. 

7.