Physics · Units, Dimensions & Error Analysis

NEET (UG) 2024 — Question 42

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:

Option A:
$\beta t / \alpha$
Option B:
$\alpha t / \beta$
Correct
Option C:
$\alpha \beta t$
Option D:
$\alpha \beta / t$

Answer: B

Step-by-step solution

From principle of homogeneity

${[F]=\left[\alpha t^{2}\right]=[\beta f]}$

${[\alpha]=\frac{[F]}{\left[t^{2}\right]} \text { and }[\beta]=\frac{[F]}{[t]}}$

$\therefore \quad[\alpha][t]=[\beta]$

$\therefore \quad \frac{\alpha t}{\beta}=$ dimensionless

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Exam: NEET (UG) 2024
Paper: 2024 paper
Subject: Physics
Chapter: Units, Dimensions & Error Analysis
Topic: Units and Dimensions Analysis

Answer: B

Step-by-step solution

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