Dimensions of the quantity frac{p}{varepsilon | vedclass

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Question

(A) We are given the quantity $\frac{p}{\varepsilon_0 \mu_0}$.We know that the speed of light in vacuum is given by $c = \frac{1}{\sqrt{\varepsilon_0

Vedclass · Accepted Answer

$[MLT^{-4}]$

Vedclass · Answer

(A) We are given the quantity $\frac{p}{\varepsilon_0 \mu_0}$.We know that the speed of light in vacuum is given by $c = \frac{1}{\sqrt{\varepsilon_0 \mu_0}}$.Squaring both sides,we get $c^2 = \frac{1}{\varepsilon_0 \mu_0}$.Substituting this into the expression,the quantity becomes $p \cdot c^2$.The dimensions of pressure $p$ are given by $\frac{	ext{Force}}{	ext{Area}} = \frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$.The dimensions of the speed of light $c$ are $[LT^{-1}]$,so the dimensions of $c^2$ are $[L^2T^{-2}]$.Therefore,the dimensions of the quantity are $[ML^{-1}T^{-2}] \cdot [L^2T^{-2}] = [MLT^{-4}]$.

$(A)$ Thermal conductivity	$(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant	(ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat	(iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat	(iv) $M^0L^2T^{-2}$

Dimensions of the quantity $\frac{p}{\varepsilon_0 \mu_0}$,where $p$ is the pressure,$\varepsilon_0$ is the electric permittivity of free space,and $\mu_0$ is the permeability of free space,will be:

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Match the following physical quantities with their respective dimensional formulas:
$(A)$ Thermal conductivity $(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant (ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat (iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat (iv) $M^0L^2T^{-2}$

Which of the following is the correct order of the fundamental forces in nature, arranged from weakest to strongest?

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