Match the List-I with List-II. The correct ma | vedclass

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Question

(B) The Boltzmann constant $k_B$ relates energy to temperature: $E = k_B T$. Thus, $[k_B] = [	ext{Energy}] / [	ext{Temperature}] = [ML^2T^{-2}] / [K

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$A-III, B-II, C-I, D-IV$

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(B) The Boltzmann constant $k_B$ relates energy to temperature: $E = k_B T$. Thus, $[k_B] = [	ext{Energy}] / [	ext{Temperature}] = [ML^2T^{-2}] / [K] = [ML^2T^{-2}K^{-1}]$. This matches $III$.
$(B)$ From Stokes' law, $F = 6\pi \eta r v$. The dimensions of viscosity $\eta$ are $[F] / ([L][LT^{-1}]) = [MLT^{-2}] / [L^2T^{-1}] = [ML^{-1}T^{-1}]$. This matches $II$.
$(C)$ Water equivalent is the mass of water that absorbs the same amount of heat as the body for the same temperature change. Its dimension is $[M]$. However, in the given options, $[ML^0T^0]$ is the closest representation of mass. This matches $I$.
$(D)$ From the heat conduction formula $Q/t = KA(	heta_1 - 	heta_2)/l$, the coefficient of thermal conductivity $K = (Q \cdot l) / (A \cdot t \cdot \Delta	heta)$. Dimensions: $[ML^2T^{-2} \cdot L] / [L^2 \cdot T \cdot K] = [MLT^{-3}K^{-1}]$. This matches $IV$.
Therefore, the correct sequence is $A-III, B-II, C-I, D-IV$.

List-$I$	List-$II$
$A$. Boltzmann constant	$I$. $[ML^0T^0]$
$B$. Coefficient of viscosity	$II$. $[ML^{-1}T^{-1}]$
$C$. Water equivalent	$III$. $[ML^2T^{-2}K^{-1}]$
$D$. Coefficient of thermal conductivity	$IV$. $[MLT^{-3}K^{-1}]$

$I$ (Fundamental forces in nature)	$II$ (Relative strength)
$(A)$ Strong nuclear force	$(e)$ $10^{-2}$
$(B)$ Weak nuclear force	$(f)$ $1$
$(C)$ Electromagnetic force	$(g)$ $10^{10}$
$(D)$ Gravitational force	$(h)$ $10^{-13}$
	$(i)$ $10^{-39}$

List-$I$	List-$II$
$A$. Coefficient of Viscosity	$I$. $[M L^2 T^{-2}]$
$B$. Surface Tension	$II$. $[M L^2 T^{-1}]$
$C$. Angular momentum	$III$. $[M L^{-1} T^{-1}]$
$D$. Rotational Kinetic energy	$IV$. $[M L^0 T^{-2}]$

List-$I$	List-$II$
$A$. Spring constant	$1$. $M^1L^2T^{-2}$
$B$. Pascal	$2$. $M^0L^0T^{-1}$
$C$. Hertz	$3$. $M^1L^0T^{-2}$
$D$. Joule	$4$. $M^1L^{-1}T^{-2}$

Similar Questions

Identify the physical parameters from the list given below that have the same dimensions:
$(i)$ Magnetic field $(B)$
$(ii)$ Energy density $(u)$
$(iii)$ Refractive index $(\mu)$
$(iv)$ Young's modulus $(Y)$
$(v)$ Dielectric constant $(K)$

Match List-$I$ with List-$II$:
List-$I$ List-$II$
$A$. Coefficient of Viscosity $I$. $[M L^2 T^{-2}]$
$B$. Surface Tension $II$. $[M L^2 T^{-1}]$
$C$. Angular momentum $III$. $[M L^{-1} T^{-1}]$
$D$. Rotational Kinetic energy $IV$. $[M L^0 T^{-2}]$

Match List-$I$ with List-$II$ and select the correct answer.

List-$I$ List-$II$

$A$. Spring constant $1$. $M^1L^2T^{-2}$

$B$. Pascal $2$. $M^0L^0T^{-1}$

$C$. Hertz $3$. $M^1L^0T^{-2}$

$D$. Joule $4$. $M^1L^{-1}T^{-2}$

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