Limitations of dimensional analysis – Rankers Physics

Dimensions: Practice Problem & Solution

Assertion (A): In mechanics the method of dimensions can't be applied to derive formula of a physical quantity which depends on more than three physical quantities. Reason (R): We can derive relation of a physical quantity with other physical quantities out of which two have same dimensions.  
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:

In mechanics, we have only three base dimensions (M, L, T). Thus, we cannot determine more than three independent exponents. If two quantities have the same dimensions, they cannot be resolved independently, making R false.

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