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Applications of Dimensional Analysis question from NEET 2024

Q17NEET 2024Easy

Applications of Dimensional Analysis

A force defined by $F = \alpha t^2 + \beta t$ acts on a particle at a given time $t$ . The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:

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Answer: (b)

Each term has dimensions of force: $[\alpha] = [F T^{-2}]$ , $[\beta] = [F T^{-1}]$ .
$[\alpha t/\beta] = \dfrac{[F T^{-2}][T]}{[F T^{-1}]} = 1$ .
So the answer is (b) $\alpha t/\beta$ .

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