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(C) To determine which pair does not have the same dimensions,we analyze each option:$(A)$ Angular momentum $(L)$ is given by $L = mvr$. Its dimension

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Moment of inertia and torque

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(C) To determine which pair does not have the same dimensions,we analyze each option:$(A)$ Angular momentum $(L)$ is given by $L = mvr$. Its dimensions are $[ML^2T^{-1}]$. Planck's constant $(h)$ is related to energy by $E = h
u$,so $[h] = [E]/[
u] = [ML^2T^{-2}]/[T^{-1}] = [ML^2T^{-1}]$. Thus,they have the same dimensions.$(B)$ Impulse $(I)$ is defined as the change in momentum,$I = \Delta p$. Thus,impulse and linear momentum have the same dimensions,$[MLT^{-1}]$.$(C)$ Moment of inertia $(I)$ has dimensions $[ML^2]$. Torque $(	au)$ is given by $	au = r 	imes F$,which has dimensions $[L] 	imes [MLT^{-2}] = [ML^2T^{-2}]$. Since $[ML^2] 
eq [ML^2T^{-2}]$,this pair does not have the same dimensions.$(D)$ Work $(W)$ is force $	imes$ displacement,$[ML^2T^{-2}]$. Torque $(	au)$ also has dimensions $[ML^2T^{-2}]$. Thus,they have the same dimensions.Therefore,the pair that does not have the same dimensions is Moment of inertia and torque.

Which of the following pairs does not have the same dimensions?

Similar Questions

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