Match the physical quantities given in List-I | vedclass

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(D) $1$. Gravitational potential: $[V] = [	ext{Energy} / 	ext{mass}] = [ML^2 T^{-2} / M] = M^0 L^2 T^{-2}$. This matches $II$.$2$. Stefan's constant

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

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(D) $1$. Gravitational potential: $[V] = [	ext{Energy} / 	ext{mass}] = [ML^2 T^{-2} / M] = M^0 L^2 T^{-2}$. This matches $II$.$2$. Stefan's constant $(\sigma)$: From $P = \sigma A T^4$, we have $[\sigma] = [P / (A T^4)] = [ML^2 T^{-3} / (L^2 K^4)] = M L^0 T^{-3} K^{-4}$. This matches $III$.$3$. Permittivity $(\varepsilon_0)$: From Coulomb's law $F = q^2 / (4 \pi \varepsilon_0 r^2)$, we have $[\varepsilon_0] = [q^2 / (F r^2)] = [(I T)^2 / (MLT^{-2} \cdot L^2)] = M^{-1} L^{-3} T^4 I^2$. This matches $IV$.$4$. Specific heat capacity $(c)$: From $Q = mc \Delta T$, we have $[c] = [Q / (m \Delta T)] = [ML^2 T^{-2} / (M \cdot K)] = M^0 L^2 T^{-2} K^{-1}$. This matches $I$.Thus, the correct matching is $A-II, B-III, C-IV, D-I$.

List-$I$	List-$II$
$A$. Gravitational potential	$I$. $M^0 L^2 T^{-2} K^{-1}$
$B$. Stefan's constant	$II$. $M^0 L^2 T^{-2}$
$C$. Permittivity	$III$. $M L^0 T^{-3} K^{-4}$
$D$. Specific heat capacity	$IV$. $M^{-1} L^{-3} T^4 I^2$

List-$I$	List-$II$
$(A)$ Torque	$(I)$ $Nms^{-1}$
$(B)$ Stress	$(II)$ $Jkg^{-1}$
$(C)$ Latent Heat	$(III)$ $Nm$
$(D)$ Power	$(IV)$ $Nm^{-2}$

$A$. $Pa \cdot s$	$(i)$. $[L^2 T^{-2} K^{-1}]$
$B$. $N \cdot m \cdot K^{-1}$	$(ii)$. $[MLT^{-3} K^{-1}]$
$C$. $J \cdot kg^{-1} \cdot K^{-1}$	$(iii)$. $[ML^{-1} T^{-1}]$
$D$. $W \cdot m^{-1} \cdot K^{-1}$	$(iv)$. $[ML^2 T^{-2} K^{-1}]$

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

List-$I$ List-$II$

$(A)$ Torque $(I)$ $Nms^{-1}$

$(B)$ Stress $(II)$ $Jkg^{-1}$

$(C)$ Latent Heat $(III)$ $Nm$

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