A force defined by F=α t^2+β t acts on a particle at a given time t . factor which is dimensionles

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1.Units, Dimensions and Measurement

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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:

A

$\alpha t / \beta$

B

$\alpha \beta t$

C

$\alpha \beta / t$

D

$\beta t / \alpha$

(NEET-2024)

Solution

From principle of homogeneity

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

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

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

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

Standard 11

Physics

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