Assertion : The dimensional formula for relat | vedclass

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(D) $1$. The relative velocity of an object $P$ with respect to $Q$ is defined as $\vec{v}_{PQ} = \vec{v}_P - \vec{v}_Q$. Since this is a vector subtr

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If the Assertion is correct but Reason is incorrect.

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(D) $1$. The relative velocity of an object $P$ with respect to $Q$ is defined as $\vec{v}_{PQ} = \vec{v}_P - \vec{v}_Q$. Since this is a vector subtraction of two velocities,the result is also a velocity. Therefore,its dimensional formula is $[M^0 L^1 T^{-1}]$,which is the same as that of velocity and the change in velocity $(\Delta v)$. Thus,the Assertion is correct.$2$. The Reason states that relative velocity is the ratio of velocities,which is physically incorrect. Relative velocity is defined as the difference between two velocities,not the ratio. Thus,the Reason is incorrect.

Column-$I$	Column-$II$
$(1)$ Torque	$(a)$ $M^1L^1T^{-1}$
$(2)$ Angular momentum	$(b)$ $M^1L^2T^{-1}$
$(3)$ Linear momentum	$(c)$ $M^1L^2T^{-2}$

$Assertion$ : The dimensional formula for relative velocity is the same as that of the change in velocity.
$Reason$ : Relative velocity of $P$ with respect to $Q$ is the ratio of the velocity of $P$ and that of $Q$.

Similar Questions

Match the physical quantities in Column-$I$ with their corresponding dimensional formulas in Column-$II$.

Column-$I$ Column-$II$

$(1)$ Torque $(a)$ $M^1L^1T^{-1}$

$(2)$ Angular momentum $(b)$ $M^1L^2T^{-1}$

$(3)$ Linear momentum $(c)$ $M^1L^2T^{-2}$

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$Assertion$ : The dimensional formula for relative velocity is the same as that of the change in velocity.$Reason$ : Relative velocity of $P$ with respect to $Q$ is the ratio of the velocity of $P$ and that of $Q$.