Question

The dimensional formula for the gravitational constant is:

• 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{ } $

Answer 1

Answer: (A)

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}}] $