Question

Which of the following is the dimensional formula for the gravitational constant? (A) 2 2 2 M L T    (B) 0 0 0 M L T (C) 2 2 2 M L T  (D) 1 3 2 M LT

Answer 1

Answer:

Dimensional Formula of Gravitational Constant

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.