Question

A unitless quantity
A) Always has non-zero dimension
B) never has a non-zero dimension
C) Does not exist
D) None of these

Answer 1

Hint: Unitless means something which doesn’t have a unit. Dimension depicts the quantity of a substance in a particular case. A substance can have a unit even if it doesn’t have a dimension. But the reverse is not true.

Complete step by step answer:
Units are used as a measure to obtain quantities in the physical world. We need units for the proper communication of information regarding physical objects. For example, in order to explain to someone how much distance we cover from our house to school, we usually use the term kilometres (km) or in some countries miles to show how much we have travelled. So the km or metre is a unit that is used to specify a physical quantity of distance.
The dimension of a physical quantity can be expressed as a product of the basic physical dimensions such as length, mass and time, each raised to a rational power.
So each physical quantity can have a dimension (ex:- force, velocity), but physical quantities can be dimensionless but still manage to have a unit, for example, an angle is obtained by the division of two lengths, so the angle has zero dimension, but it has a unit which we usually denote by radian. So dimensionless physical quantities can have units. When considering unitless quantities it is impossible for them to have any dimension, since a unitless quantity does not have dimensions.
So the answer to the question is option (B)- Never has a non-zero dimension.

Note: Not all quantities require a unit of their own. Using physical laws we can say that units of quantities can be expressed as combinations of units of other quantities therefore only a small set of units is required. These units are taken as the base units and the other units are derived units.
The base units are the units of the quantities which are independent of other quantities and they are the units of length, mass, time, electric current, temperature, luminous intensity and the amount of substance.
Derived units are the units of the quantities which are derived from the base quantities and some of the derived units are the units of speed, work, acceleration, energy, pressure etc.