A) \[\left[ {{M}^{-1}}{{L}^{2}}{{T}^{-2}} \right]~\]
B) \[\left[ {{M}^{0}}{{L}^{0}}{{T}^{0}} \right]\]
C) \[\left[ {{M}^{-1}}{{L}^{3}}{{T}^{-2}} \right]~\]
D) \[\left[ {{M}^{-1}}{{L}^{3}}{{T}^{-1}} \right]\]
Correct Answer: C
Solution :
\[F=\frac{G{{M}_{1}}{{M}_{2}}}{{{R}^{2}}}\] \[\Rightarrow \]\[G=\frac{F{{R}^{2}}}{{{M}_{1}}{{M}_{2}}}\] \[\therefore \]\[[G]=\frac{[ML{{T}^{-2}}][{{L}^{2}}]}{[{{M}^{2}}]}=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
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