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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.

List-$I$	List-$II$
$A$. Spring constant	$1$. $M^1L^2T^{-2}$
$B$. Pascal	$2$. $M^0L^0T^{-1}$
$C$. Hertz	$3$. $M^1L^0T^{-2}$
$D$. Joule	$4$. $M^1L^{-1}T^{-2}$

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	$(IV)$ $[M^1 L^1 T^{-3} A^{-1}]$

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

Similar Questions

The graph between two quantities $P$ and $Q$ is a straight line passing through the origin when:

Match List-$I$ with List-$II$ and select the correct answer.

List-$I$ List-$II$

$A$. Spring constant $1$. $M^1L^2T^{-2}$

$B$. Pascal $2$. $M^0L^0T^{-1}$

$C$. Hertz $3$. $M^1L^0T^{-2}$

$D$. Joule $4$. $M^1L^{-1}T^{-2}$

Match the following. (Take the relative strength of the strongest fundamental forces in nature as $1$)

Write the unit and dimensional formula of the ratio of the gravitational constant $(G)$ to the acceleration due to gravity $(g)$.

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