# Which of the following statements about the universal gravitational…

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## Which of the following statements about the universal gravitational constant G is true?

A. It is a fundamental quantity

B. It has dimension M⁻¹L³T⁻²

C. Its S.I. unit is Nm²kg

D. It is a vector quantity

B

## DETAILS…

The universal gravitational constant G has a dimension of M⁻¹L³T⁻², it can be derived as below…

F = Gm₁m₂/r²

m₁g = Gm₁m₂/r²

m₁gr² = Gm₁m₂

G = m₁gr²/m₁m₂

G = gr²/m₂

Transforming into dimensions, we have:

g = LT⁻²

r = L

m = M

G = LT⁻²× L²/M

G =LT⁻²L²M⁻¹

G = M⁻¹L³T⁻²

### Now for the right answer to the above question:

1. Option A is incorrect. it is not a fundamental quantity but a derived quantity.
2. Option B is correct. its dimension is derived as M⁻¹L³T⁻².
3. C is incorrect. the S.I. unit will be Nm²kg⁻² and not Nm²kg.
4. D is not the correct answer. it is not a vector but a scalar quantity.

## KEY-POINTS…

You may please note these/this:

• Gravitational constant G has a dimension of M⁻¹L³T⁻².
• Gravitational constant G has a unit of Nm²kg⁻² or kg⁻¹m³s⁻².
• Gravitational constant is a scalar quantity.

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/ culled from 2021 JAMB-UTME PHYSICS question 23 BATCH-B /