Question

A unitless quantity?
A. Does not exist
B. Always has a nonzero dimension
C. Never has a nonzero dimension
D. May have a nonzero dimension

Answer 1

Hint: The dimension of a physical quantity is the power to which the fundamental quantities are raised in order to obtain the unit of a physical quantity.

Complete step-by-step solution:
The dimension of a physical quantity is defined as the powers to which the fundamental quantities are raised so as to represent that physical quantity and there are seven fundamental quantities which are named as length, mass, time, temperature, electric current, luminous intensity, and amount of substance.
A unitless quantity is the one in which fundamental quantities are not involved and it doesn't have any unit hence it doesn't have any dimensions so their dimension is Zero.
For example, if we take $\pi $ which is the ratio of the perimeter of the circle to its diameter and its mathematical value i.e. $ \simeq 3.14$ approx but it does not have any unit and does not have any dimension.
Let's take another example i.e. probability which is the ratio of the number of favorable outcomes to the number of total outcomes, so probability also does not have any unit and also not having any dimension.
Therefore from these examples, it is clear that a unitless quantity exists and they have zero dimensions.
Hence the correct option is C i.e. a unitless quantity never has a nonzero dimension.

Note: Actually a dimensionless quantity can have a unit, like in the case of angle (radian) but the opposite of this is not true, means a unitless quantity can never have dimensions basically it is the unit that gives dimensions to something.