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 statement is false for the angular momentum $\vec{L}$ about the origin?

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$\vec{L} = mv [\frac{R}{\sqrt{2}} + a] \hat{k}$ When the particle is moving from B to C

$\vec{L} = \frac{mv}{\sqrt{2}} R \hat{k}$ When the particle is moving from D to A

$\vec{L} = - \frac{mv}{\sqrt{2}} R \hat{k}$ When the particle is moving from A to B

$\vec{L} = mv [\frac{R}{\sqrt{2}} + a] \hat{k}$ When the particle is from C to D

answer is B.

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Detailed Solution

$\vec{L} = m (\vec{r} \times \vec{v})$

Correct statement should be

$\vec{L} = - \frac{mv}{\sqrt{2}} R \hat{k}$ When the particle is moving from D to A

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