The dimensions of gravitational constant are

Options

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

Correct answer

D. $\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$

Step-by-step solution

From the formula

G=\frac{F R^2}{m_1 m_2}

\begin{aligned} & G=\frac{\text{ Dimensions of dimensions of force } F \times \text{ dimension of }(R)^2}{\text{ dimensions of mass } M \times \text{ dimension of mass } M} \end{aligned}

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

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