If electronic charge $e$, electron mass $m$, speed of light in vacuum $c$ and Planck 's constant $h$ are taken as fundamental quantities, the permeability of vacuum $\mu _0$ can be expressed in units of

  • [JEE MAIN 2015]
  • A

    $\left( {\frac{h}{{m{e^2}}}} \right)$

  • B

    $\left( {\frac{{hc}}{{m{e^2}}}} \right)$

  • C

    $\left( {\frac{h}{{c{e^2}}}} \right)$

  • D

    $\left( {\frac{{m{c^2}}}{{h{e^2}}}} \right)$

Similar Questions

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?

$(1)$ The dimension of force is $L ^{-3}$

$(2)$ The dimension of energy is $L ^{-2}$

$(3)$ The dimension of power is $L ^{-5}$

$(4)$ The dimension of linear momentum is $L ^{-1}$

  • [IIT 2019]

The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be

  • [JEE MAIN 2021]

The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are

  • [JEE MAIN 2023]

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Density of wood is $0.5 \;gm / cc$ in the $CGS$ system of units. The corresponding value in $MKS$ units is.?