Question

Give two examples of dimensionless variables.

Answer 1

Hint: A dimensionless variable is the unit-less value which is produced by multiplying and dividing the combinations may be repeated of the physical variable, parameters and the constants.

Complete step by step answer:
a.) Coefficient of Friction – It is the force which resists or opposes the motion of one body with another body in contact with it. It is denoted by $$\mu$$ .
It can be expressed as –
$\mu ={\displaystyle \frac{F}{N}}$
Where, $\mu =$ Coefficient of friction
$F=$ Frictional Force
$N=$ Normal force
Since both the frictional force and the normal force have the same units, they cancel each other in the ratio. And therefore we get the unit of coefficient of friction ($\mu$ ) unit-less. Most of the materials have the coefficient of friction ranging between zero and one.
b.) Relative density – it is the ratio of the density of a substance with the density of the given specific reference material. It is also known as the specific gravity.
It can be expressed as –
$RD={\displaystyle \frac{{\rho }_{subs\tan ce}}{{\rho }_{reference}}}$
Where, RD is the relative density
${\rho }_{subs\tan ce}=$ Density of the substance to be measured
${\rho }_{reference}=$ Density of the reference material
Since density is measured in gram per centimetre cube or kilogram per metre cube, both the units cancel each other in the above ratio and therefore relative number is just the number without any units.

Note:
Always remember that the unit does not mean a physical unit. As a result, there are dimensionless quantities which will always be independent of the basic units such as meter, second, kilograms, Kelvin or the ampere and many more. But in the exemption, there are physical quantities which are dimensionless but still have a unit. For example, Angle has the unit “radian”. Since it is the ratio of two lengths it is defined as the dimensionless quantity.