Question

Derive the formula for the universal law of gravitation

Answer 1

Answer:-

Every object in this universe attracts every other object towards it.

Newton gave a law which states that the gravitational force between the two bodies depends on their masses and the separation between them.

This is called universal law of gravitation or newton's law of gravitation.

According to this law of gravitation, the force F between two bodies is :-

1: Directly proportional to the product of their masses.

2: Inversely proportional to the square of the distance between their centres.

Formula:-

F = Gm1m2 / r ^2

DERIVATION:-

ME = 100 MM ------ I

RE= 16RM --------- II

From Universal Law of Gravitation

F = GMm / R ^2

W = GMm / R^2

F = W

WE = GME * M / RE ^ 2 ---- III

WM = GMm * M / RM^2 ---- IV

WE / WM = (GME * M / R^2 ) / (GMm * M / RM ^ 2)

WE / WM = GME * m / RE^2 * RM^2 / GMM * m

Putting the value from eq. i and ii

WE / WM = G100Mm * M / 16RM^2 * RM^2/ GMm * M

WE/ WM = 100 /6

WE/WM = 6

WE = 6WM

WM = 1/6 WE

Answer 2

Answer:

Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.