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The physical quantity having the dimensions $\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^3 \mathrm{~A}^2\right]$ is
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The correct answer is:
electrical conductivity
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
$\sigma=\frac{1}{\rho}$
$[\sigma]=\frac{1}{[\rho]}=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~A}^2 \mathrm{~T}^3\right]$
$\begin{aligned} \because \quad[\mathrm{p}] & =\frac{[\mathrm{M}]}{\left[\mathrm{L}^{-3}\right][\mathrm{AT}]^2[\mathrm{~T}]} \\ & =\left[\mathrm{ML}^3 \mathrm{~A}^{-2} \mathrm{~T}^{-3}\right]\end{aligned}$
So, electrical conductivity
$\sigma=\frac{1}{\rho}$
$[\sigma]=\frac{1}{[\rho]}=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~A}^2 \mathrm{~T}^3\right]$
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