Dimensional Analysis

Question

If gravitational potential energy between two masses is U = - G m_1 m_2 / r, what are dimensions of G?

RankGuru · Accepted Answer

Rearranging the formula to solve for the Universal Gravitational Constant $G$:
$G = \frac{U \cdot r}{m_1 \cdot m_2}$
Now, substitute the dimensions of each quantity:
- $[U]$ (Energy) = $[ML^2 T^{-2}]$
- $[r]$ (Distance) = $[L]$
- $[m_1, m_2]$ (Mass) = $[M]$
$[G] = \frac{[ML^2 T^{-2}] \cdot [L]}{[M] \cdot [M]} = \frac{[ML^3 T^{-2}]}{[M^2]} = [M^{-1} L^3 T^{-2}]$.

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