MCQ
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:
- ✓$\alpha t / \beta$
- B$\alpha \beta t$
- C$\alpha \beta / t$
- D$\beta t / \alpha$
✓
Answer
Correct option: A.
$\alpha t / \beta$
a
From principle of homogeneity
From principle of homogeneity
${[F]=\left[\alpha t^2\right]=[\beta t]}$
${[\alpha]=\frac{[F]}{\left[t^2\right]} \text { and }[\beta]=\frac{[F]}{[t]}}$
$\therefore \quad[\alpha][t]=[\beta]$
$\therefore \quad \frac{\alpha t}{\beta}=\text { dimensionless }$
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