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

Question:

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

  1. MLT $^{-2} \mathrm{~K}$

  2. $\mathrm{MLT}^{-2} \mathrm{~K}^{-2}$

  3. $\mathrm{MLT}^{-3} \mathrm{~K}$

  4. $\mathrm{MLT}^{-3} \mathrm{~K}^{-1}$

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

JEE Main Previous Year 2020


Correct Option: 4

Solution:

$\begin{aligned}$

$&\text {  From formula, } \frac{d Q}{d t}=k A \frac{d T}{d x} \\$

$&\Rightarrow k=\frac{\left(\frac{d Q}{d t}\right)}{A\left(\frac{d T}{d x}\right)} \\$

$&{[k]=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-3}\right]}{\left[\mathrm{L}^{2}\right]\left[\mathrm{KL}^{-1}\right]}=\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]}$

$\end{aligned}$

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

  • 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

Leave a Reply

Your email address will not be published.

error: Content is protected !!
Download App