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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.

List-$I$	List-$II$
$A$. Coefficient of Viscosity	$I$. $[M L^2 T^{-2}]$
$B$. Surface Tension	$II$. $[M L^2 T^{-1}]$
$C$. Angular momentum	$III$. $[M L^{-1} T^{-1}]$
$D$. Rotational Kinetic energy	$IV$. $[M L^0 T^{-2}]$

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

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Match List-$I$ with List-$II$:
List-$I$ List-$II$
$A$. Coefficient of Viscosity $I$. $[M L^2 T^{-2}]$
$B$. Surface Tension $II$. $[M L^2 T^{-1}]$
$C$. Angular momentum $III$. $[M L^{-1} T^{-1}]$
$D$. Rotational Kinetic energy $IV$. $[M L^0 T^{-2}]$

$A$ wheel completes $2000$ revolutions to cover a distance of $9.5\, km$. The diameter of the wheel is:

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