Question

find expression for unit G and also its dimensional formula.​

Answer 1

Answer:

G = [M1 L1 T-2] × [L]2 × [M]-2

G = [M-1 L3 T-2].

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

Explanation:

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Answer 2

Answer:

I'm not sure if I will be able to explain it perfectly but I'll try-

We know gravitational force F= G Mm/ r²

( here both m values denote mass and r denotes distance between the two masses )

The reason we use this equation is because it is the easiest way to reduce G to the three fundamental units of mass, length and time.

Now, G= F r²/ m²

We know that F= ma ( where a = acceleration )

a= v/ t ( where v= velocity, t= time )

v= l/t ( where l= distance )

So, a = l/ t²

F= m× l/ t²

Let us now go back and substitute this in the big equation.

G= m× l/ t² × l²/ m² ( I have taken r² as l² as both represent distance. )

⇒G = m/ m² × l × l² × 1/ t²= m⁻¹ l³ t⁻²

Representing it as dimensional formula, we get-

G= M⁻¹ L³ T⁻²