Which of the following is a dimensional constant ?

The correct answer is gravitational constant.

To understand why, let us define what a dimensional constant is and analyze each of the options provided:

Dimensional Constant:
A physical quantity that has a constant numerical value but possesses physical dimensions is called a dimensional constant.

Let us analyze the given options:

1. Relative density:
Relative density is defined as the ratio of the density of a substance to the density of water. Since it is a ratio of two identical physical quantities (densities), the dimensions cancel out. Therefore, it is a dimensionless variable.
$\text{Relative Density}=\frac{\text{Density of substance}}{\text{Density of water}}$

2. Gravitational constant:
According to Newton's law of universal gravitation, the force ($F$) between two masses ($m_1$ and $m_2$) separated by a distance ($r$) is given by:
$F=\frac{G{m}_1{m}_2}{r^2}$
Rearranging the formula for the universal gravitational constant ($G$):
$G=\frac{F{r}^2}{m_1{m}_2}$
Substituting the dimensional formulas for force, distance, and mass:
$\left[G\right]=\frac{\left[{\mathrm{MLT}}^{-2}\right]\left[L^2\right]}{\left[M^2\right]}=\left[M^{-1}{L}^3{T}^{-2}\right]$
Since the universal gravitational constant has a constant value and also possesses dimensions, it is a dimensional constant.

3. Refractive index:
Refractive index is the ratio of the speed of light in a vacuum to the speed of light in a medium. Being a ratio of two speeds, it is a dimensionless quantity.
$\text{Refractive Index}=\frac{\text{Speed of light in vacuum}}{\text{Speed of light in medium}}$

4. Poisson's ratio:
Poisson's ratio is the ratio of lateral strain to longitudinal strain. Since it is a ratio of two strains (which are themselves dimensionless ratios of lengths), it is a dimensionless quantity.

Thus, among the given choices, the only dimensional constant is the gravitational constant.