Relation between gravitation and gravity!!!
What is gravitation?
Gravitation is the phenomenon of force of attraction between any two bodies.
What is gravity?
The force of attraction between earth and anyone body.
Relation:
Condition: An object that lies in the Earth's crust.
Let us consider mass of the earth as 'M'.
Let us consider mass of the object(that we consider here) as 'm'.
Let us consider the radius of the earth as 'R'.
Let us consider the radius of the object (that we consider here) as 'r'.
The force of attraction between earth and any body can be calculated as follow:
The force of gravitation = G × product of masses (mass of earth and any object) / sq. of distance (r²)
Note: distance (here) - the distance between the centre of the earth to the centre of the object that we consider here. However, here we consider only the radius of the earth since the radius of any object that we consider is negligible to the radius of earth.
The force of gravitation = G × Mm / R²
According to the Newton's second law of motion, force can also be calculated by 'mass(m) ×acceleration(a)'
The force of gravitation = m(mass of the object) × a (acceleration of the object)
The force of gravitation = m(mass of the object) × g (acceleration of the object)
The force of gravitation = m × g
We have named 'a' as 'g(gravity)' since g is constant everywhere in earth
The force of gravitation = G × Mm / R² ---- 1
The force of gravitation = m × g ---- 2
Equate 1 and 2
m × g = G × Mm / R²
g = G × M / R² ---- 3
Mass of the earth(M) can be calculated by density of earth(ρ) and volume of the earth(v).
M = ρ v ---- 4
Volume of the earth(v) is equal to product of 4/3 and π and R³
v = 4/3 × π × R³ ---- 5
Substitute 5 in 4
M = ρ × 4/3 π R³ ---- 6
Substitute 6 in 3
g = (G ρ × 4/3 π R³) / R²
g = G ρ (4/3) π R
Relation: g = G ρ (4/3) π R
Relation:
Condition: An object that lies in the Earth's crust.
Let us consider mass of the earth as 'M'.
Let us consider mass of the object(that we consider here) as 'm'.
Let us consider the radius of the earth as 'R'.
Let us consider the radius of the object (that we consider here) as 'r'.
The force of attraction between earth and any body can be calculated as follow:
The force of gravitation = G × product of masses (mass of earth and any object) / sq. of distance (r²)
Note: distance (here) - the distance between the centre of the earth to the centre of the object that we consider here. However, here we consider only the radius of the earth since the radius of any object that we consider is negligible to the radius of earth.
The force of gravitation = G × Mm / R²
According to the Newton's second law of motion, force can also be calculated by 'mass(m) ×acceleration(a)'
The force of gravitation = m(mass of the object) × a (acceleration of the object)
The force of gravitation = m(mass of the object) × g (acceleration of the object)
The force of gravitation = m × g
We have named 'a' as 'g(gravity)' since g is constant everywhere in earth
The force of gravitation = G × Mm / R² ---- 1
The force of gravitation = m × g ---- 2
Equate 1 and 2
m × g = G × Mm / R²
g = G × M / R² ---- 3
Mass of the earth(M) can be calculated by density of earth(ρ) and volume of the earth(v).
M = ρ v ---- 4
Volume of the earth(v) is equal to product of 4/3 and π and R³
v = 4/3 × π × R³ ---- 5
Substitute 5 in 4
M = ρ × 4/3 π R³ ---- 6
Substitute 6 in 3
g = (G ρ × 4/3 π R³) / R²
g = G ρ (4/3) π R
Relation: g = G ρ (4/3) π R
