A) \[[{{M}^{-1}}\,{{L}^{3}}\,{{T}^{-2}}]\]
B) \[[M{{L}^{2}}\,{{T}^{-1}}]\]
C) \[[{{M}^{-2}}\,{{L}^{3}}\,{{T}^{-2}}]\]
D) \[[{{M}^{-2}}\,{{L}^{2}}\,{{T}^{-1}}]\]
Correct Answer: A
Solution :
Key Idea: Substitute the dimensions for the quantities involved in an expression written for gravitational constant. According to Newton's law of gravitation, the force of attraction between two masses \[{{m}_{1}}\] and\[{{m}_{2}}\] separated by a distance r is, \[F=\frac{G\,\,\,{{m}_{1}}\,{{m}_{2}}}{{{r}^{2}}}\Rightarrow G=\frac{F{{r}^{2}}}{{{m}_{1}}{{m}_{2}}}\] Substituting the dimensions for the quantities on the right hand side, we obtain dimensions of \[G=\frac{[ML{{T}^{-2}}][{{L}^{2}}]}{[{{M}^{2}}]}\] \[=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
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