Units and Dimensions – Rankers Physics

Dimensions: Practice Problem & Solution

Assertion (A): If a physical quantity has a unit it must have dimension. Reason (R): There may exist a physical quantity which has dimension but no 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

Short Solution (Best for NEET):

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

An angle has a unit (radian) but is dimensionless, so A is false. Any physical quantity that possesses dimensions must have a unit, so R is also false.

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