# In SI units, the dimensions of $\sqrt{\frac{\epsilon_{0}}{\mu_{0}}}$ is

Question:

In SI units, the dimensions of $\sqrt{\frac{\epsilon_{0}}{\mu_{0}}}$ is

1. (a) $\mathrm{A}^{-1} \mathrm{TML}^{3}$

2. $\mathrm{AT}^{2} \mathrm{M}^{-1} \mathrm{~L}^{-1}$

3. $\mathrm{AT}^{-3} \mathrm{ML}^{3 / 2}$

4. $\mathrm{A}^{2} \mathrm{~T}^{3} \mathrm{M}^{-1} \mathrm{~L}^{-2}$

JEE Main Previous Year Single Correct Question of JEE Main from Chemistry Laws of Motion chapter.

JEE Main Previous Year 2019

Correct Option: 4

Solution:

$\left[\sqrt{\frac{\varepsilon_{0}}{\mu_{0}}}\right]=\sqrt{\frac{\varepsilon_{0}^{2}}{\mu_{0} \varepsilon_{0}}}=\left[\frac{\varepsilon_{0}}{\sqrt{\mu_{0} \varepsilon_{0}}}\right]=\varepsilon_{0} C\left[L T^{-1}\right] \times\left[\varepsilon_{0}\right]$

$\because F=\frac{q^{2}}{4 \pi \varepsilon_{0} r^{2}}$

$\left.\Rightarrow\left[\varepsilon_{0}\right]=\frac{1}{[A T]^{2}}=C\right]$

$\therefore\left[\sqrt{\frac{\varepsilon_{0}}{\mu_{0}}}\right]=\left[L T^{-1}\right] \times\left[A^{2} M^{-1} L^{-3} T^{4}\right]$

$=\left[M^{-1} L^{-2} T^{3} A^{2}\right]$

### Related Questions

• The density of a material in SI unit is $128 \mathrm{~kg} \mathrm{~m}^{-3} .$ In certain units in which the unit of length is $25 \mathrm{~cm}$ and the unit of mass is $50 \mathrm{~g}$, the numerical value of density of the material is:

View Solution

• A metal sample carrying a current along $X$-axis with density $J_{x}$ is subjected to a magnetic field $\mathrm{B}_{\mathrm{z}}$ (along z-axis). The electric field $E_{y}$ developed along Y-axis is directly proportional to $J_{x}$ as well as $\mathrm{B}_{Z}$. The constant of proportionality has SI unit

View Solution

• The quantities $x=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}, y=\frac{E}{B}$ and $z=\frac{1}{C R}$ are defined where $C$-capacitance, $R$-Resistance, $l$-length, $E$-Electric field, $B$-magnetic field and $\varepsilon_{0}, \mu_{0},-$ free space permittivity and permeability respectively. Then :

View Solution

• Dimensional formula for thermal conductivity is (here $K$ denotes the temperature:

View Solution

• Dimensional formula for thermal conductivity is (here $K$ denotes the temperature:

View Solution

• A quantity $x$ is given by $\left(I F v^{2} / W L^{4}\right)$ in terms of moment of inertia $I$, force $F$, velocity $v$, work $W$ and Length $L$. The dimensional formula for $x$ is same as that of :

View Solution

• Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

View Solution

• If speed $\mathrm{V}$, area $\mathrm{A}$ and force $\mathrm{F}$ are chosen as fundamental units, then the dimension of Young’s modulus will be :

View Solution

• If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is:

View Solution

• Which of the following combinations has the dimension of electrical resistance $\left(\epsilon_{0}\right.$ is the permittivity of vacuum and $\mu_{o}$ is the permeability of vacuum)?

View Solution

error: Content is protected !!