dimensional formula (gravitational constant)

Question

Dimensions of universal gravitational constant G?

RankGuru · Accepted Answer

1. **Formula**: Newton’s law of universal gravitation is $F = G \frac{m_1 m_2}{r^2}$.
2. **Isolate G**: $G = \frac{F r^2}{m_1 m_2}$.
3. **Dimensions**:
   - $F$ (Force) $= [MLT^{-2}]$
   - $r^2$ (Distance squared) $= [L^2]$
   - $m_1 m_2$ (Mass product) $= [M^2]$
4. **Combine terms**:
   - $[G] = \frac{[MLT^{-2}][L^2]}{[M^2]}$
   - $[G] = [M^{1-2} L^{1+2} T^{-2}] = [M^{-1} L^3 T^{-2}]$.
5. **Result**: The dimensional formula is **$[M^{-1} L^3 T^{-2}]$**.

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dimensional formula (gravitational constant)

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