Unitless and dimensionless quantities – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Dimensions

Unitless and dimensionless quantities


Assertion (A): A unitless quantity never has a non-zero dimension.
Reason (R): A dimensionless quantity never has a unit.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

A quantity without a unit is always dimensionless, so A is true. However, a dimensionless quantity can have a unit (for example, plane angle has the unit radian), making R false.

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