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(B) The dimensions of the given physical quantities are as follows:$A$. Angular momentum $(L = mvr)$ and Planck's constant $(h = E/f)$ both have dimen

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Moment of inertia and moment of a force

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(B) The dimensions of the given physical quantities are as follows:$A$. Angular momentum $(L = mvr)$ and Planck's constant $(h = E/f)$ both have dimensions $[M L^2 T^{-1}]$.$B$. Moment of inertia $(I = mr^2)$ has dimensions $[M L^2]$. Moment of a force (Torque,$	au = r 	imes F$) has dimensions $[M L^2 T^{-2}]$. These are not identical.$C$. Work $(W = F \cdot d)$ and torque $(	au = r 	imes F)$ both have dimensions $[M L^2 T^{-2}]$.$D$. Impulse $(J = F \Delta t)$ and momentum $(p = mv)$ both have dimensions $[M L T^{-1}]$.Therefore,the pair that does not have identical dimensions is Moment of inertia and moment of a force.

$A$. 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-$I$	List-$II$
$(1)$ Planck's constant	$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant	(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus	(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity	(iv) $[M^{-1} L^3 T^{-2}]$

Out of the following,the only pair that does not have identical dimensions is

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