dimensional analysis (g)

Question

Dimensions of G are?

RankGuru · Accepted Answer

1. **Formula**: Start from $F = G \frac{m_1 m_2}{r^2}$.
2. **Isolate G**: $G = \frac{F r^2}{m_1 m_2}$.
3. **Units Calculation**:
   - Force ($F$): $[MLT^{-2}]$
   - Distance squared ($r^2$): $[L^2]$
   - Mass squared ($m^2$): $[M^2]$
4. **Dimension Analysis**: $[G] = \frac{[MLT^{-2}][L^2]}{[M^2]} = M^{1-2} L^{1+2} T^{-2}$.
5. **Final Result**: **$[G] = [M^{-1} L^{3} T^{-2}]$**.

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dimensional analysis (g)

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