The dimension of the universal constant of gravitation, \(G\), is
\([\mathrm{M^{-1}L^3T^{-2}}]\)
Newton's law of gravitation: \(F = \frac{Gm_1m_2}{r^2}\), so \(G = \frac{Fr^2}{m_1m_2}\).
Dimensions: \([F] = [\mathrm{MLT^{-2}}]\), \([r^2] = [\mathrm{L^2}]\) and \([m_1m_2] = [\mathrm{M^2}]\).
Therefore \([G] = \frac{[\mathrm{MLT^{-2}}][\mathrm{L^2}]}{[\mathrm{M^2}]} = [\mathrm{M^{-1}L^3T^{-2}}]\).
Check: in SI units \(G = 6.67\times10^{-11}\ \mathrm{N\,m^2\,kg^{-2}} = 6.67\times10^{-11}\ \mathrm{m^3\,kg^{-1}\,s^{-2}}\), which matches.
Hence, the answer is \([\mathrm{M^{-1}L^3T^{-2}}]\).
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