A) \[M{{L}^{3}}{{T}^{-2}}\]
B) \[{{M}^{-1}}{{L}^{2}}{{T}^{-2}}\]
C) \[M{{L}^{-2}}{{T}^{2}}\]
D) \[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}\]
Correct Answer: D
Solution :
From the formula\[G=\frac{F{{R}^{2}}}{{{m}_{1}}{{m}_{2}}}\] Dimensions of \[\text{G=}\frac{\text{dimensions}\,\,\text{of}\,\,\text{force}\,\,\text{F }\!\!\times\!\!\text{ dimensions}\,\,\text{of}\,\,{{\text{(R)}}^{\text{2}}}}{\text{dimension}\,\,\text{of}\,\,\text{mass}\,\,\text{M }\!\!\times\!\!\text{ dimension}\,\,\text{of}\,\,\text{mass}\,\,\text{M}}\] \[=\frac{[ML{{T}^{-2}}][{{L}^{2}}]}{[M][M]}=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
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