The dimensions of universal gravitational constant are

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Accepted Answer

The Universal Gravitational Constant ($G$) is defined by Newton's Law of Gravitation: $F = G rac{m_1 m_2}{r^2}$.

1.  **Rearranging for G:**
    $$G = rac{F 	imes r^2}{m_1 	imes m_2}$$

2.  **Dimensional Analysis:**
    *   Force ($F$) = Mass $	imes$ Acceleration = $[M] 	imes [LT^{-2}] = [MLT^{-2}]$
    *   Distance ($r$) = $[L]$
    *   Mass ($m$) = $[M]$

3.  **Substituting Dimensions:**
    $$[G] = rac{[MLT^{-2}] 	imes [L]^2}{[M] 	imes [M]}$$
    $$[G] = rac{[ML^3T^{-2}]}{[M^2]}$$
    $$[G] = [M^{1-2} L^3 T^{-2}] = [M^{-1}L^3T^{-2}]$$

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