Which of following is not a dimensionless quantity?

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1.Units, Dimensions and Measurement

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Which of the following is not a dimensionless quantity?

A

Relative magnetic permeability $\left(\mu_{{r}}\right)$

B

Power factor

C

Permeability of free space $\left(\mu_{0}\right)$

D

Quality factor

(JEE MAIN-2021)

Solution

$\left[\mu_{{}}\right]=1 \text { as } \mu_{{r}}=\frac{\mu}{\mu_{{m}}}$

[power factor $(\cos \phi)]=1$

$\mu_T{0}=\frac{{B}_{0}}{{H}}\left(\right.$ unit $\left.={NA}^{-2}\right)$ : Not dimensionless

$\left[\mu_{0}\right]=\left[{MLT}^{-2} {A}^{-2}\right]$

quality factor (Q) $=\frac{\text { Energystored }}{\text { Energy dissipated per cycle }}$

So $Q$ is unitless $\&$ dimensionless.

Standard 11

Physics

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