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