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

Vedclass · Answer

$(D)$. 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	$IV$. $MLT^{-3} K^{-1}$

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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: