Question

find the dimension of gravitational constant ¿¿¿​

Answer 1

The dimensional formula of gravitational constant is given by,

M-1 L3 T-2

Where,

M = Mass

L = Length

T = Time

Derivation

From Newton’s law of gravitation,

Force (F) = [GmM] × r-2

Gravitational Constant (G) = F × r2 × [Mm]-1 . . . . (1)

Since, Force (F) = Mass × Acceleration = M × [LT-2]

∴ The dimensional formula of force = M1 L1 T-2 . . . . (2)

On substituting equation (2) in equation (1) we get,

Gravitational Constant (G) = F × r2 × [Mm]-1

Or, G = [M1 L1 T-2] × [L]2 × [M]-2 = [M-1 L3 T-2].

Therefore, the gravitational constant is dimensionally represented as M-1 L3 T-2.

Answer 2

Answer:

According to the Universal Law of Gravitation, 

F = GMm/r²

⟹ G = Fr²/Mm

⟹ [G] = [Fr²/Mm]

= [MLT‐²] [L²]

[M²]

= [M‐¹L³T‐²]

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