The physical quantities that have the same di | vedclass

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Question

(D) To determine which quantities have the same dimensions,we analyze their dimensional formulas:$1$. Work $(W)$ is defined as force $	imes$ displace

Vedclass · Accepted Answer

Work and torque

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(D) To determine which quantities have the same dimensions,we analyze their dimensional formulas:$1$. Work $(W)$ is defined as force $	imes$ displacement. Its dimension is $[ML^2T^{-2}]$.$2$. Torque $(	au)$ is defined as force $	imes$ perpendicular distance. Its dimension is $[ML^2T^{-2}]$.$3$. Since both work and torque have the same dimensional formula $[ML^2T^{-2}]$,they are the physical quantities with the same dimensions.$4$. Other options: Force is $[MLT^{-2}]$,Power is $[ML^2T^{-3}]$,Latent heat is $[L^2T^{-2}]$,and Specific heat is $[L^2T^{-2}K^{-1}]$. Thus,only Work and Torque match.

List $I$	List $II$
$P.$ Boltzmann constant	$1.$ $[ML^2T^{-1}]$
$Q.$ Coefficient of viscosity	$2.$ $[ML^{-1}T^{-1}]$
$R.$ Planck constant	$3.$ $[MLT^{-3}K^{-1}]$
$S.$ Thermal conductivity	$4.$ $[ML^2T^{-2}K^{-1}]$

List $I$	List $II$
$A$. Torque	$I$. $[M^1 L^1 T^{-2} A^{-2}]$
$B$. Magnetic field	$II$. $[L^2 A^1]$
$C$. Magnetic moment	$III$. $[M^1 T^{-2} A^{-1}]$
$D$. Permeability of free space	$IV$. $[M^1 L^2 T^{-2}]$

Column-$I$	Column-$II$
$(a)$ Wien's constant	$(i)$ $W m^{-2} K^{-4}$
$(b)$ Stefan-Boltzmann's constant	$(ii)$ $W m^{-1} K^{4}$
	$(iii)$ $m K$

The physical quantities that have the same dimensions are:

Similar Questions

Match List $I$ with List $II$:

List $I$ List $II$

$A$. Torque $I$. $[M^1 L^1 T^{-2} A^{-2}]$

$B$. Magnetic field $II$. $[L^2 A^1]$

$C$. Magnetic moment $III$. $[M^1 T^{-2} A^{-1}]$

$D$. Permeability of free space $IV$. $[M^1 L^2 T^{-2}]$

Choose the correct answer from the options given below:

The phenomenon of physics that deals with the constitution and structure of matter at the minute scales of atoms and nuclei is

If $\epsilon_0$,$E$,and $t$ represent the free space permittivity,electric field,and time respectively,then the unit of $\frac{\epsilon_0 E}{t}$ will be:

Units for constants in Column-$I$ and $SI$ unit is given in Column-$II$. Match the followings:

Column-$I$ Column-$II$

$(a)$ Wien's constant $(i)$ $W m^{-2} K^{-4}$

$(b)$ Stefan-Boltzmann's constant $(ii)$ $W m^{-1} K^{4}$

$(iii)$ $m K$

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