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JIPMER 2011
Exam
JIPMER
Year
2011
Subject
Physics
Chapter
Units and Dimensions

JIPMER 2011 · Physics · Units and Dimensions

The physical quantity having the dimensions [M^ -1 ~L^ -3 ~T^3...

The physical quantity having the dimensions [M−1 L−3 T3 A2]\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^3 \mathrm{~A}^2\right] is

Options

  1. Aresistance
  2. Bresistivity
  3. Celectrical conductivity
  4. Delectromotive force

Correct answer

C. electrical conductivity

Step-by-step solution

Resistivity, ρ=mne2τ\rho=\frac{m}{n e^2 \tau}∵[p]=[M][L−3][ AT ]2[ T]=[ML3 A−2 T−3]\begin{aligned} \because \quad[\mathrm{p}] & =\frac{[\mathrm{M}]}{\left[\mathrm{L}^{-3}\right][\mathrm{\text{ AT }}]^2[\mathrm{~T}]} \\ & =\left[\mathrm{ML}^3 \mathrm{~A}^{-2} \mathrm{~T}^{-3}\right]\end{aligned}$$ So, electrical conductivity \sigma=\frac{1}{\rho} [\sigma]=\frac{1}{[\rho]}=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~A}^2 \mathrm{~T}^3\right]
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