JAMB Physics 2015 Paper

Concept:Use Newton’s law of gravitation to express $G$ in terms of force, mass, and distance.Explanation:Newton’s law of gravitation is:$$F = \frac{G m_1 m_2}{r^2}$$Make $G$ the subject of the formula:$$G = \frac{F r^2}{m_1 m_2}$$Write each quantity in fundamental dimensions:Force: $F = MLT^{-2}$Distance squared: $r^2 = L^2$Product of masses: $m_1 m_2 = M^2$Substitute these into the expression:$$G = \frac{MLT^{-2} \times L^2}{M^2}$$Simplify:$$G = M^{-1}L^3T^{-2}$$Answer:The dimension of the universal gravitational constant is Option A: $M^{-1}L^3T^{-2}$.