A) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{\text{-1}}}{{\text{L}}^{\text{3}}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
B) \[\text{ }\!\![\!\!\text{ ML}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
C) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{2}}{{\text{T}}^{-2}}\text{ }\!\!]\!\!\text{ }\]
D) \[\text{ }\!\![\!\!\text{ }{{\text{M}}^{-1}}{{\text{L}}^{3}}\text{T }\!\!]\!\!\text{ }\]
Correct Answer: A
Solution :
Gravitational constant is equal in magnitude to that force of attraction which acts between two particles each of unit mass separated by a unit distance apart. \[\therefore \] \[G=\frac{F{{r}^{2}}}{{{m}_{1}}{{m}_{2}}}\] (Newtons law of gravitation) where \[{{m}_{1}}\]and \[{{m}_{2}}\]are masses, r is the distance between them, and F is force. \[\therefore \] Dimensions of gravitational constant \[\text{=}\,\,\frac{\text{dimensions}\,\text{of}\,\text{force}\,\,\text{ }\!\!\times\!\!\text{ }\,{{\text{(length)}}^{\text{2}}}}{{{\text{(dimensions}\,\text{of}\,\text{mass)}}^{\text{2}}}}\] \[=\frac{[ML{{T}^{-2}}][{{L}^{2}}]}{[{{M}^{2}}]}\] \[=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
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