Question

write universal law of gravitation and its symbols​

Answer 1

This law states that two objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The symbol ɡ should not be confused with G, the gravitational constant, or g, the symbol for gram. The ɡ is also used as a unit for any form of acceleration, with the value defined as above; see g-force.

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Answer 2

Here is your answer,

Every body in this universe attracts each other with a force whose magnitude is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This force acts along the line joining the centres of two bodies.

Now, consider two bodies of masses m₁ and m₂ with their centres mutually separated by a distance r. So, the force( in magnitude) of gravitational attraction between two bodies.

According to Newton's Law of Motion:-

F α m₁m₂ ----------------> (1)

and F α 1/r² ---------------> (2)

From equation (1) and (2)

F α m₁m₂/r²

Gravitational force, F = G m₁m₂/r² ------------------->(3)

where G is constant of proportionality known as gravitational constant. It is also known as universal gravitational constant.

In CGS system, the value of G is 6.67×10⁻⁸ dyne cm² g⁻² and its SI value is 6.67×10 Nm² kg⁻²

DIMENSIONAL FORMULA FOR G

G= F r²/m₁m₂ = [ MLT⁻² ] [ L² ]/[M²]

= [ MLT⁻² ] [L³ [ [ M⁻² ]

= [ M⁻¹ L ³T⁻² ]

Now suppose, m = m = 1 unit and r = 1 unit, then from Eq (3)

F = G ×1 ×1/(1)² = F = G

Thus, universal gravitational constant (G) is numerically equal to the force of attraction acting between two bodies each of unit mass by unit distance apart.