Question

The dimensions of universal gravitational constant are

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

Answer 1

Answer: (A)

$[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]$

Answer 2

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 $G=\frac{\left[ MLT ^{-2}\right]\left[ L ^{2}\right]}{\left[ M ^{2}\right]}$ $=\left[ M ^{-1} L ^{3} T ^{-2}\right]$