A) \[[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
B) \[[ML{{T}^{-2}}]\]
C) \[[M{{L}^{2}}{{T}^{-2}}]\]
D) \[[{{M}^{-1}}{{L}^{-3}}T]\]
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 \[=\frac{dimensions\text{ }of\text{ }force\times {{(length)}^{2}}}{{{(dimensions\text{ }of\text{ }mass)}^{2}}}\] \[=\frac{[ML{{T}^{-2}}]\,[{{L}^{2}}]}{[{{M}^{2}}]}\] \[=[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]
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