Newton’s Law of Gravitation Formula
Statement:- According to Newton’s, “every object in the universe attracts every other object with a force. This force is directly proportional to the product of mass and inertly proportional to the square of the distance between them”.
Consider the two objects of masses m1 and m2 and these two objects separated by distance d.
From the statement, mathematically, the gravitational force of attraction between two object can be written as,
F ∝ m1m2 —- (1)
F ∝ 1/d2 ——- (2)
Combine equation (1) & (2)
F ∝ m1m2/d2
F = G m1m2/d2 —— (3)
Where, G is the constant of proportional and called the Universal gravitational constant. The SI unit of G is N m2/kg2
From formula (3) the value of G becomes,
G = Fd2/m1m2
From this formula we can calculate the gravitation constant as well as force. The experimentally measured value G is 6.673 × 10-11 Nm2/kg2
Numericals on Newton’s Law of Gravitation Formula:
Consider a two objects of mass 25 kg and 30 kg respectively. These two objects are separated by distance 1 m. What is gravitational force between them?
Given: d = 1m
m1 = 25 kg
m2 = 80 kg
and G = 6.67 × 10-11 Nm2/kg2
F = Gm1m2/d2
F = 6.67×10-11×25×30/12
F = 5, 002.5×10-11
F = 5.0025×10-7 N
The gravitational force between these two objects is 5.0025×10-7 N.