In SI units,the dimensions of sqrt {frac{{{va | vedclass

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(C) The dimensions of permittivity of free space $\varepsilon_0$ are $[M^{-1} L^{-3} T^4 A^2]$.The dimensions of permeability of free space $\mu_0$ ar

Vedclass · Accepted Answer

$A^2 T^3 M^{-1} L^{-2}$

Vedclass · Answer

(C) The dimensions of permittivity of free space $\varepsilon_0$ are $[M^{-1} L^{-3} T^4 A^2]$.The dimensions of permeability of free space $\mu_0$ are $[M L T^{-2} A^{-2}]$.Therefore,the dimensions of $\sqrt{\frac{\varepsilon_0}{\mu_0}}$ are:$\left[ \sqrt{\frac{\varepsilon_0}{\mu_0}} \right] = \left[ \frac{M^{-1} L^{-3} T^4 A^2}{M L T^{-2} A^{-2}} \right]^{1/2}$$= \left[ M^{-1-1} L^{-3-1} T^{4-(-2)} A^{2-(-2)} \right]^{1/2}$$= \left[ M^{-2} L^{-4} T^6 A^4 \right]^{1/2}$$= [M^{-1} L^{-2} T^3 A^2]$.

List $I$	List $II$
$A$. Spring constant	$I$. $(T^{-1})$
$B$. Angular speed	$II$. $(MT^{-2})$
$C$. Angular momentum	$III$. $(ML^2)$
$D$. Moment of inertia	$IV$. $(ML^2T^{-1})$

Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

In $SI$ units,the dimensions of $\sqrt {\frac{{{\varepsilon _0}}}{{{\mu _0}}}} $ are:

Similar Questions

In $SI$ units,$kg m^2 s^{-2}$ is equivalent to which of the following?

Out of the following pairs,which one does not have identical dimensions?

Match List $I$ with List $II$:
List $I$ List $II$
$A$. Spring constant $I$. $(T^{-1})$
$B$. Angular speed $II$. $(MT^{-2})$
$C$. Angular momentum $III$. $(ML^2)$
$D$. Moment of inertia $IV$. $(ML^2T^{-1})$

Choose the correct answer from the options given below:

Define dimensional formula and dimensional equation by using suitable examples.

Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$

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