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(C) To determine which pair does not have the same dimensions,we analyze each option:$A$. Inductance $(L)$ has dimensions $[M L^2 T^{-2} A^{-2}]$,whil

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Moment of Inertia and Moment of Force

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(C) To determine which pair does not have the same dimensions,we analyze each option:$A$. Inductance $(L)$ has dimensions $[M L^2 T^{-2} A^{-2}]$,while Momentum $(p = mv)$ has dimensions $[M L T^{-1}]$. These are not the same.$B$. Work $(W = F \cdot d)$ has dimensions $[M L^2 T^{-2}]$,and Torque $(	au = r 	imes F)$ also has dimensions $[M L^2 T^{-2}]$. These are the same.$C$. Moment of Inertia $(I = mr^2)$ has dimensions $[M L^2]$,and Moment of Force $(	au = r 	imes F)$ has dimensions $[M L^2 T^{-2}]$. These are not the same.$D$. Angular Momentum $(L = mvr)$ has dimensions $[M L^2 T^{-1}]$,and Planck's constant $(h = E/f)$ also has dimensions $[M L^2 T^{-1}]$. These are the same.Note: The question asks for pairs that do not have the same dimensions. Both $A$ and $C$ satisfy this. However,in standard physics problems of this type,$C$ is the most common intended answer as it compares two distinct physical quantities often confused in introductory mechanics.

Select the pair from the following that does not have the same dimensions.

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