Unitless and dimensionless quantities – Rankers Physics

Dimensions: Practice Problem & Solution

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 Explained:

To solve this problem, we apply the core principles of Dimensions. Understanding the underlying formula is key to arriving at the correct answer below:

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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1. If \(E\) and \(G\) respectively denote energy and gravitational constant, then \(\frac{E}{G}\) has the dimensions of: [2021]
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