Question

Which of the following is a dimensional constant?

• A. Refractive index
• B. Possions ratio
• C. Stress
• D. Gravitaional constant

Answer 1

The correct option is D Gravitaional constant

A) Refractive index:- It is the ratio of velocity of light in a vacuum to its velocity in specified medium.

$\mu =\frac{c}{v}$

$\left[\mu \right]=\frac{\left[c\right]}{\left[v\right]}=\frac{\left[M^0{L}^0{T}^{-1}\right]}{\left[M^0{L}^1{T}^{-1}\right]}$

Hence, refractive index is dimensionless quantity.

B) Passions ratio:- The ratio of the proportional decreases in a lateral measurement to the proportional increases in length in a sample of the material that is elastically stretched.

Hence, it is dimensionless quantity.

C) Stress:- It is the ratio of force to the area.

$s=\frac{F}{A}$

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

It is not a dimensionless quantity. But it is not a constant value.

D) Gravitational constant:- It is a universal constant, denoted by $G$.

$G=6.674\times {10}^{-11}{m}^3/kg{s}^2$

Dimensional value, $\left[G\right]=\left[M^{-1}{L}^3{T}^{-2}\right]$

The correct option is D.