Which of the following statements about the universal gravitational…
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
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 = gr²/m₂
Transforming into dimensions, we have:
g = LT⁻²
r = L
m = M
G = LT⁻²× L²/M
G = M⁻¹L³T⁻²
Now for the right answer to the above question:
- Option A is incorrect. it is not a fundamental quantity but a derived quantity.
- Option B is correct. its dimension is derived as M⁻¹L³T⁻².
- C is incorrect. the S.I. unit will be Nm²kg⁻² and not Nm²kg.
- D is not the correct answer. it is not a vector but a scalar quantity.
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 /