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JEE Main 202127 AugustMorning Shift
Exam
JEE Main
Year
2021
Date
27 August
Shift
Morning Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2021 · 27 August · Morning Shift · Physics · Units and Dimensions

Which of the following is not a dimensionless quantity?

Which of the following is not a dimensionless quantity?

Options

  1. APower factor
  2. BQuality factor
  3. CPermeability of free space (μ0)\left({\mu}_{0}\right)
  4. DRelative magnetic permeability (μr)\left({\mu}_{r}\right)

Correct answer

C. Permeability of free space (μ0)\left({\mu}_{0}\right)

Step-by-step solution

The power factor is defined as,cosϕcosϕ which is dimensionless, the formula of quality factor, Q=1RLCQ = \dfrac{1}{R}\sqrt{\dfrac{L}{C}}, which is also dimensionless, and the permeability in free space, μr=μμ0{\mu}_{r} = \dfrac{\mu}{{\mu}_{0}}, but permeability in free space is defined as, μ0=c2ε0{\mu}_{0} = \dfrac{{c}^{2}}{{ε}_{0}}, here cc is the speed of light in vacuum and ε0{ε}_{0} is the permittivity in free space so this having dimension.
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