The physical quantity having the dimensions [M^-1 ~L^-3 ~T^3 ~A^2 ] is

Correct answer: (C) electrical conductivity. Resistivity, ρ=m/(n e^2 τ) ∵ [p] =frac[M] [L^-3 ][AT]^2[~T] = [ML^3 ~A^-2 ~T^-3 ] So, electrical conductivity σ=1/(ρ) [σ]=1/([ρ])= [M^-1 ~L^-3 ~A^2 ~T^3 ]

Q84 / 160 · JIPMER 2011 · Physics

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

A
resistance
B
resistivity
Correct answer
C
electrical conductivity
D
electromotive force

Solution

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

Hence, the correct answer is option: 'C'.

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

Solution

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