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Physics · PYQ NEET UG 2024
हिन्दीA 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:
Correct answer · Option 4
\( \frac{\alpha t}{\beta} \)
Explanation
From dimensional homogeneity, \( [\alpha t^2] = [\beta t] \implies [\alpha] t^2 = [\beta] t \implies \frac{[\alpha] t}{[\beta]} = 1 \). Thus, \( \frac{\alpha t}{\beta} \) is dimensionless.
