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 :
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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