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.

$Assertion$ : 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 $Q$.

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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 $Q$.