Question

A dimensionless quantity:
A. May have a unit
B. Never has a unit
C. Always has a unit
D. Does not exist

Answer 1

Hint: Physical quantities as the seven dimensions of the physical world, which are denoted with square brackets []. Thus, length has the dimension [L], mass [M], time [T], electric current [A], dynamic temperature [k] and amount of substance [mol]. Note using the square brackets round a quantity means that we are dealing with ‘the dimensions of’ the quantity. The nature of a physical quantity is described by its dimensions.

Complete step-by-step answer:
We know that, unit for angle is radian but can you guess its dimension? No, it doesn't have dimension but it has units. Like this there are many more and we will do this in detail.
The dimension of a physical quantity is the power to which the base quantities are raised to represent that quantity.
In mechanics, all the physical quantities can be returned in terms of dimensions [L],[M],[T]. For example, the volume occupied by an object is expressed as the product of Length, breadth and height or 3 lengths. Hence the dimensions of the volume are [L][L][L] =${{\left[ L \right]}^{3}}$= $\left[ {{L}^{3}} \right]$. As the volume is independent of mass and time, it is said to possess zero dimension in mass$\left[ {{M}^{0}} \right]$, zero dimension in time $\left[ {{T}^{0}} \right]$ and three dimension in length. Similarly, forces is the product of mass and acceleration and can be expressed as
Force = mass × acceleration
\[force=mass\times \left( length \right)/{{\left( time \right)}^{2}}\]
The dimensions of force are$\left[ M \right]\left[ L \right]/{{\left[ T \right]}^{2}}=[ML{{T}^{-2}}]$. Thus, force has one dimension in length, one dimension in length and -2 dimension in time the dimension in all other base quantities is zero.
So the answer is may have the unit.

Answer is (A)

Note: In this type of representation, the magnitude is not considered. It is the quality of the type of physical quantity which is expressed by using dimension. Do not get confused between raised to the power and power used on the head of the letter. Both are equal. But generally, dimensions are written under the bracket.