The dimensions of universal gravitational constant are

The correct option is M⁻¹L³T⁻².

Let us derive the dimensions of the universal gravitational constant ($G$) step-by-step using Newton's law of universal gravitation.

According to Newton's law of gravitation, the gravitational force ($F$) between two masses ($m_1$ and $m_2$) separated by a distance ($r$) is given by the formula:
$F=\frac{G{m}_1{m}_2}{r^2}$

To find the dimensions of $G$, we rearrange the equation as follows:
$G=\frac{F{r}^2}{m_1{m}_2}$

Now, let us write down the dimensions of each quantity involved in the equation:
1. Force ($F$) = Mass × Acceleration, so its dimensional formula is:
$\left[F\right]=\left[ML{T}^{-2}\right]$
2. Distance ($r$) has the dimension of length:
$\left[r\right]=\left[L\right]$, and thus $\left[r^2\right]=\left[L^2\right]$
3. Masses ($m_1$ and $m_2$) have the dimension of mass:
$\left[m_1\right]=\left[m_2\right]=\left[M\right]$

Substituting these dimensions into the expression for $G$:
$\left[G\right]=\frac{\left[ML{T}^{-2}\right]\times \left[L^2\right]}{\left[M\right]\times \left[M\right]}$

Simplifying the expression:
$\left[G\right]=\frac{\left[M{L}^3{T}^{-2}\right]}{\left[M^2\right]}$

Combining the terms of mass ($M$):
$\left[G\right]=\left[M^{-1}{L}^3{T}^{-2}\right]$

Thus, the dimensional formula of the universal gravitational constant is indeed M⁻¹L³T⁻².