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 :

Question:

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 :

1. $x, y$ and $z$ have the same dimension.

2. Only $x$ and $z$ have the same dimension.

3. Only $x$ and $y$ have the same dimension.

4. Only $y$ and $z$ have the same dimension.

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

JEE Main Previous Year 2020

Correct Option: 1

Solution:

We know that

Speed of light, $c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}=x$

Also, $c=\frac{E}{B}=y$

Time constant, $\tau=R c=t$

$\therefore z=\frac{l}{R c}=\frac{l}{t}=\text { Speed }$

Thus, $x, y, z$ will have the same dimension of speed.

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

• 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

• In the formula $\mathrm{X}=5 \mathrm{YZ}^{2}, \mathrm{X}$ and $\mathrm{Z}$ have dimensions of capacitance and magnetic field, respectively. What are the dimensions of $\mathrm{Y}$ in SI units ?

View Solution

error: Content is protected !!