Dimensional analysis is applied to derive formulae, to check dimensional consistency of equations an

Question

Dimensional analysis is applied to derive formulae, to check dimensional consistency of equations and to deduce relation among the physical quantities. To convert one system of units into another system of units, we use the relation\ $n_{2}=n_{1}\left(\frac{M_{1}}{M_{2}}ight)^{a}\left(\frac{L_{1}}{L_{2}}ight)^{b}\left(\frac{T_{1}}{T_{2}}ight)^{c}$\ where $M_{1}, L_{1}, T_{1}$ are fundamental units in one system; $M_{2}, L_{2}, T_{2}$ are fundamental units in the other system, $a, b, c$ are the dimensions of the quantity in mass, length and time, $n_{1}$ is numerical value in one system and $n_{2}$ is its numerical value in the other system.\ The only mechanical quantity which has negative dimension of mass is\

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(d): Gravitational constant $(G)=\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$ Thus, gravitational constant has negative dimension of mass.