Question

derive formula for universal law of gravitation.​

Answer 1

Answer:The Universal Law of Gravitation is stated below:

"Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects."

Explanation:

Let two objects A and B of masses M and m lie at a distance d from each other. Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is,

F M*m ---------- (1)

And the force between two objects is inversely proportional to the square of the distance between them, that is,

F α 1 ⁄ d2 ---------- (2)

Combining Eqs. (1) and (2), we get

F α M x m ⁄ d2 ---------- (3)

or, F = G( (M x m) ⁄ d2) ---------- (4)

where G is the constant of proportionality and is called the universal gravitation constant. By multiplying crosswise, Eq. (4) gives

F × d 2 = G M × m

or G = F d2/ M m ---------- (5)

The SI unit of G can be obtained by substituting the units of force, distance and mass in Eq. (5) as N m2 kg–2.

The value of G was found out by Henry Cavendish (1731 – 1810) by using a sensitive balance. The accepted value of

G is 6.673 × 10–11 N m2 kg–2.