Match List-I with List-II and choose the corr | vedclass

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Question

(A) The dimensional formulas for the given constants are as follows:
$A$. Boltzmann constant $(k_B)$: Since $E = k_B T$, the dimension is $[ML^2T^{-2

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The dimensional formulas for the given constants are as follows:
$A$. Boltzmann constant $(k_B)$: Since $E = k_B T$, the dimension is $[ML^2T^{-2}K^{-1}]$. This matches $III$.
$B$. Stefan's constant $(\sigma)$: Since $I = \sigma T^4$, where $I$ is intensity $(MT^{-3})$, the dimension is $[MT^{-3}K^{-4}]$. This matches $IV$.
$C$. Planck's constant $(h)$: Since $E = h
u$, the dimension is $[ML^2T^{-1}]$. This matches $II$.
$D$. Gravitational constant $(G)$: Since $F = G(m_1m_2)/r^2$, the dimension is $[M^{-1}L^3T^{-2}]$. This matches $I$.
Therefore, the correct matching is $A-III, B-IV, C-II, D-I$.

List-$I$	List-$II$
$A$. Boltzmann constant	$I$. $[M^{-1}L^3T^{-2}]$
$B$. Stefan's constant	$II$. $[ML^2T^{-1}]$
$C$. Planck's constant	$III$. $[ML^2T^{-2}K^{-1}]$
$D$. Gravitational constant	$IV$. $[ML^0T^{-3}K^{-4}]$

$A$. Entropy	$I$. Angular velocity
$B$. Young's modulus of elasticity	$II$. Boltzmann constant
$C$. Angular momentum	$III$. Energy density
$D$. Decay constant	$IV$. Planck's constant

List $I$ (Physical Quantity)	List $II$ (Dimensional Formula)
$(A)$ Pressure gradient	$(I)$ $[M^0 L^2 T^{-2}]$
$(B)$ Energy density	$(II)$ $[M^1 L^{-1} T^{-2}]$
$(C)$ Electric Field	$(III)$ $[M^1 L^{-2} T^{-2}]$
$(D)$ Latent heat	$(IV)$ $[M^1 L^1 T^{-3} A^{-1}]$

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