A) \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{3}}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
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 :
Key Idea: From definition, 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. Numerically, gravitational constant \[G=\frac{F{{r}^{2}}}{{{m}_{1}}{{m}_{2}}}\] where F is force, r is the distance between the two masses \[{{m}_{1}}\]and \[{{m}_{2}}.\] Writing the dimensions of all the quantities in the above formula, the dimensions of G are \[[G]=\frac{[ML{{T}^{-2}}][{{L}^{2}}]}{[M][M]}=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
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