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 $[ML^{-1}T^{-2}] \cdot [L^2T^{-2}] = [MLT^{-4}]$.

$LIST$-$I$	$LIST$-$II$
$A$. Planck's constant	$I$. $ML^2T^{-2}$
$B$. Stopping potential	$II$. $T^{-1}$
$C$. Work function	$III$. $ML^2T^{-1}$
$D$. Threshold frequency	$IV$. $ML^2T^{-3}A^{-1}$

List-$I$	List-$II$
$(i)$ Curie	$(A)$ $MLT^{-2}$
$(ii)$ Light year	$(B)$ $M$
$(iii)$ Dielectric strength	$(C)$ Dimensionless
$(iv)$ Atomic weight	$(D)$ $T$
$(v)$ Decibel	$(E)$ $ML^2T^{-2}$
	$(F)$ $MT^{-3}$
	$(G)$ $T^{-1}$
	$(H)$ $L$
	$(I)$ $MLT^{-3}I^{-1}$
	$(J)$ $LT^{-1}$

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:

Similar Questions

Match the following physical quantities in $LIST$-$I$ with their dimensional formulas in $LIST$-$II$:
$LIST$-$I$ $LIST$-$II$
$A$. Planck's constant $I$. $ML^2T^{-2}$
$B$. Stopping potential $II$. $T^{-1}$
$C$. Work function $III$. $ML^2T^{-1}$
$D$. Threshold frequency $IV$. $ML^2T^{-3}A^{-1}$

Which of the following pairs of physical quantities have the same dimensions,where one is a vector and the other is a scalar?

Which year was declared as the International Year of Physics?

Identify the incorrect statement.

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