A particle of mass m is moving along the side | vedclass

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(D) The angular momentum is given by $\vec L = \vec r 	imes \vec p = r_{\perp} p \hat n$,where $r_{\perp}$ is the perpendicular distance from the ori

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Both $(b)$ and $(c)$

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(D) The angular momentum is given by $\vec L = \vec r 	imes \vec p = r_{\perp} p \hat n$,where $r_{\perp}$ is the perpendicular distance from the origin to the line of motion.For segment $A$ to $B$: The line of motion is $y = R/\sqrt{2}$. The perpendicular distance is $R/\sqrt{2}$. The velocity is in $+x$ direction,so $\vec L = (R/\sqrt{2})mv(-\hat k)$.For segment $B$ to $C$: The line of motion is $x = R/\sqrt{2} + a$. The perpendicular distance is $R/\sqrt{2} + a$. The velocity is in $+y$ direction,so $\vec L = (R/\sqrt{2} + a)mv(\hat k)$.For segment $C$ to $D$: The line of motion is $y = R/\sqrt{2} + a$. The perpendicular distance is $R/\sqrt{2} + a$. The velocity is in $-x$ direction,so $\vec L = (R/\sqrt{2} + a)mv(\hat k)$.For segment $D$ to $A$: The line of motion is $x = R/\sqrt{2}$. The perpendicular distance is $R/\sqrt{2}$. The velocity is in $-y$ direction,so $\vec L = (R/\sqrt{2})mv(\hat k)$.Comparing these with the options,statements $(b)$ and $(c)$ are false.

$A$ particle of mass $m$ is moving along the side of a square of side '$a$',with a uniform speed $v$ in the $x-y$ plane as shown in the figure. Which of the following statements is false for the angular momentum $\vec L$ about the origin?

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