Question

Which of the following is a dimensional constant?
A. Refractive Index
B. Dielectric constant
C. Relative density
D. Gravitational constant

Answer 1

Hint: The physical quantities which have dimensions and have a fixed value are called dimensional constant. To get the answer for this question, get the dimension of each of the terms in the options using their formula. If you know the formula, then it is easy for you to know if the options mentioned have a dimension or not.

Complete solution:
Refractive Index is defined as the relative speed at which light moves through a material with respect to its speed in vacuum. As both the values belong to the same quantity (speed), units get nullified.
So the Refractive Index is a dimensionless quantity.
Dimensional Formula of Refractive Index = $M^0{L}^0{T}^0$.
If $C$ is the value of the capacitance of a capacitor filled with a given dielectric and $C_0$ is the capacitance of an identical capacitor in a vacuum, the dielectric constant, symbolized by the Greek letter kappa, $\kappa$, is simply expressed as :
$\kappa =C/C_0$.
The dielectric constant is a number without dimensions.
Relative density of a substance is defined as the density of a substance divided by the density of water. Hence, it is a pure ratio and has no dimensions. Therefore, relative density is dimensionless.
A gravitational coupling constant is a constant characterizing the gravitational attraction between a given pair of elementary particles. Therefore, the dimension of the gravitational constant is $M^{-1}{L}^3{T}^{-2}$ .

Therefore, the correct answer is Option (D).

Note:
To get the solution for this question, you should know the definition and formula of the terms given in the option such that it becomes easy to derive the dimension of the constant from the formula and also it helps to understand which constant has dimension and which constant is dimensionless.