Question

The dimensions of gravitational constant G are:

• A. $\left[ ML ^{3} T ^{-2}\right]$
• B. $\left[ M ^{-1} L ^{2} T ^{-2}\right]$
• C. $\left[ ML ^{-2} T ^{-2}\right]$
• D. $\left[ M ^{-1} L ^{3} T ^{-2}\right]$

Answer 1

Answer: (D)

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}}] $