WAEC Physics 2021 Paper

Concept:$G$ is the universal gravitational constant that appears in Newton's law of gravitation and is a derived scalar quantity.Explanation:Newton's law of gravitation is $F = \frac{G m_1 m_2}{r^2}$.So, $G = \frac{F r^2}{m_1 m_2}$.Force has SI unit $\mathrm{N}$, distance $r$ has unit $\mathrm{m}$, and mass has unit $\mathrm{kg}$.Therefore, the SI unit of $G$ is $\mathrm{N\,m^2\,kg^{-2}}$, not $\mathrm{N\,m^2\,kg}$.Using dimensions: $F = MLT^{-2}$, $r^2 = L^2$, and $m_1 m_2 = M^2$.Thus, the dimension of $G$ is $\frac{(MLT^{-2})(L^2)}{M^2} = M^{-1}L^3T^{-2}$.$G$ is a scalar quantity because it has no direction, and it is not a fundamental quantity.So, the only true statement is option B.Answer:B. It has dimension $M^{-1}L^3T^{-2}$.