Q. Dimensional formula for the universal gravitational constant $G$ is
A) $\left\lbrack M^{- 1}L^{2}T^{- 2} \right\rbrack$
B) $\left\lbrack M^{0}L^{0}T^{0} \right\rbrack$
C) $\left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack$
D) $\left\lbrack M^{- 1}L^{3}T^{- 1} \right\rbrack$
Explanation
Gravitational force, $F = \frac{GM_{1}M_{2}}{R^{2}}$ $\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ G = \frac{FR^{2}}{M_{1}M_{2}}$ $\lbrack G\rbrack = \frac{\left\lbrack MLT^{- 2} \right\rbrack\left\lbrack L^{2} \right\rbrack}{\left\lbrack M^{2} \right\rbrack}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.