Newton’s Law of Gravitation Formula and Numericals on it

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.

Updated: August 19, 2021 — 2:37 am

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