Match the List-I with List-II:List-IList-IIA. | vedclass

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$(D)$. Spring constant $(k)$: From $F = kx$, we have $[k] = [F]/[x] = [MLT^{-2}]/[L] = [ML^0 T^{-2}]$. Thus, $A-II$.$B$. Thermal conductivity $(k)$: F

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

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$(D)$. Spring constant $(k)$: From $F = kx$, we have $[k] = [F]/[x] = [MLT^{-2}]/[L] = [ML^0 T^{-2}]$. Thus, $A-II$.$B$. Thermal conductivity $(k)$: From $dQ/dt = kA(\Delta T/l)$, we have $[k] = [ML^2 T^{-3}][L]/([L^2][K]) = [MLT^{-3} K^{-1}]$. Thus, $B-IV$.$C$. Boltzmann constant $(k_B)$: From $E = (3/2)k_B T$, we have $[k_B] = [E]/[T] = [ML^2 T^{-2}]/[K] = [ML^2 T^{-2} K^{-1}]$. Thus, $C-I$.$D$. Inductive reactance $(X_L)$: $X_L = \omega L$. The dimension is the same as resistance $(R = V/I)$. $[R] = [ML^2 T^{-3} A^{-2}]$. Thus, $D-III$.Therefore, the correct matching is $A-II, B-IV, C-I, D-III$.

List-$I$	List-$II$
$A$. Spring constant	$I$. $ML^2 T^{-2} K^{-1}$
$B$. Thermal conductivity	$II$. $ML^0 T^{-2}$
$C$. Boltzmann constant	$III$. $ML^2 T^{-3} A^{-2}$
$D$. Inductive reactance	$IV$. $MLT^{-3} K^{-1}$

List-$I$	List-$II$
$(A)$ Torque	$(I)$ $kg\,m^{-1}\,s^{-2}$
$(B)$ Energy density	$(II)$ $kg\,m\,s^{-1}$
$(C)$ Pressure gradient	$(III)$ $kg\,m^{-2}\,s^{-2}$
$(D)$ Impulse	$(IV)$ $kg\,m^2\,s^{-2}$

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

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Match List-$I$ with List-$II$.

List-$I$ List-$II$

$(A)$ Torque $(I)$ $kg\,m^{-1}\,s^{-2}$

$(B)$ Energy density $(II)$ $kg\,m\,s^{-1}$

$(C)$ Pressure gradient $(III)$ $kg\,m^{-2}\,s^{-2}$

$(D)$ Impulse $(IV)$ $kg\,m^2\,s^{-2}$

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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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Match the List-$I$ with List-$II$:List-$I$List-$II$$A$. Spring constant$I$. $ML^2 T^{-2} K^{-1}$$B$. Thermal conductivity$II$. $ML^0 T^{-2}$$C$. Boltzmann constant$III$. $ML^2 T^{-3} A^{-2}$$D$. Inductive reactance$IV$. $MLT^{-3} K^{-1}$Choose the correct answer from the options given below: