🌍 Acceleration Due to Gravity (g)

🔹 Definition

The acceleration due to gravity is the acceleration produced in a body when it is freely falling towards the Earth under the influence of Earth’s gravitational force.

• It is denoted by g.

• Near the Earth’s surface, its average value is 9.8 m/s².

This means that the velocity of a freely falling body increases by about 9.8 m/s every second in the absence of air resistance.

🔹 Derivation: Relation of g with Distance from Earth’s Center

The universal law of gravitation gives the force between the Earth and a body of mass m as:

F=GMm/r2​

Where:

• G = Universal gravitational constant

• M = Mass of the Earth

• r = Distance between the center of the Earth and the body

From Newton’s second law:

F=mg

Equating the two forces:

mg=GMm/r2​

Cancelling m:

g=GM/r2​

🔹 Important Points

1. At the surface of the Earth
   r=R(radius of Earth)

   g=GM/R2​

2. At a height (h) above the surface
   r=R+h

   gh=GM/(R+h)2​

3. At the center of the Earth
   Effectively, g=0 because all forces cancel out.

🔹 Conclusion

• The value of g decreases as the distance from the Earth’s center increases.

• Near the surface, g≈9.8 m/s2.

• This explains why objects weigh less on mountains or in space compared to sea level.