Question

A) Give an example of physical quantity which has a unit but no dimensions.

B) Give an example of a Physical quantity which has neither unit nor dimensions.

C) Give an example of a constant which has a unit

D) Give an example of a constant which has no unit

Answer 1

A) Solid angle $(\Omega$) : it is the ratio of subtended area on sphere to radius squared.

$\Omega =\frac{A}{r^2}$ steradian

Plane angle $(\Theta$) : it is the ratio of subented arc length on circle to radius

$\Theta =\frac{l}{r}$ radian.


B) Relative density : Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material.

Specific gravity = $\frac{densityofmedium}{densityofwater{4}^{0}c}$

It is ratio of two same quantites. So, it is a unitless and dimensionless constant.

Final answer: Relative density etc.

C) The gravitational force F between two masses $m_{1}and{m}_2$ at distance r is given by

F= $\frac{G{m}_1{m}_2}{r^2}$ $\Rightarrow$ G = $\frac{F{r}^2}{m_1{m}_2}$
Where, G = Gravitational constant = $6.67\times {10}^{-}11N{m}^2/k{g}^2$

Final Answer: Gravitational constant


D) Reynolds number: The Reynolds number is the ratio of inertial forces to viscous forces within a fluid remains constant for a particular fluid flow problem. So, the Reynolds number has no units.
Final Answer : Reynolds number