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(D) The angular momentum of a particle about an origin $O$ is given by $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$. The magnitude i

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It increases as it moves towards the line $BC$.

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(D) The angular momentum of a particle about an origin $O$ is given by $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$. The magnitude is $L = mvr \sin 	heta = mv d$,where $d$ is the perpendicular distance from the origin to the line of motion.$1$. For motion along $OA$,the line of motion passes through the origin $O$,so $d = 0$ and $L = 0$. Statement $A$ is correct.$2$. For the line $DE$,the perpendicular distance from $O$ to the line $DE$ is constant $(1 \ m)$. Thus,$L$ is constant at all points on $DE$. Statement $B$ is correct.$3$. At $B$,the perpendicular distance is $1 \ m$ and the velocity is in the $+y$ direction. At $D$,the perpendicular distance is $1 \ m$ and the velocity is in the $+x$ direction. The angular momentum is a vector quantity. The direction of $\vec{L}$ at $B$ is $\vec{r} 	imes \vec{v} = (1\hat{i}) 	imes (v\hat{j}) = mv\hat{k}$. The direction of $\vec{L}$ at $D$ is $\vec{r} 	imes \vec{v} = (1\hat{j}) 	imes (v\hat{i}) = -mv\hat{k}$. Thus,they have the same magnitude but opposite directions. Statement $C$ is correct.$4$. As the particle moves towards the line $BC$,the perpendicular distance $d$ from the origin $O$ to the line of motion remains constant. Therefore,the angular momentum does not change. Statement $D$ is incorrect.

$A$ particle of mass $m$ moves with a constant velocity. Which of the following statements is incorrect regarding its angular momentum?

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