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 : <br> <br> Which of the following statements is false for the angular momentum $\overrightarrow{L}$ about the origin ?

Question

( A ) $\overrightarrow{L} = -\frac{mv}{2} \;R \;\hat{k}$ when the particle is moving from A to B
( B ) $\overrightarrow{L} = mv [\frac{R}{\sqrt{2}} + a ] \hat{k}$ when the particle is moving from C to D.
( C ) $\overrightarrow{L} = -\frac{mv}{\sqrt{2}} \;R \;\hat{k}$ when the particle is moving from A to B
( D ) $\overrightarrow{L} = mv [\frac{R}{\sqrt{2}} - a ] \hat{k}$ when the particle is moving from C to D.