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 $\overrightarrow {L}$ about the origin?

Question

$\begin{array}{1 1} (1)\overrightarrow {L} = -\large\frac{mv}{\sqrt 2} \normalsize R \hat k \text{When the particle is moving from A to B} \\ (2)\overrightarrow {L} =mv \bigg[\large\frac{R}{\sqrt 2} \normalsize a \bigg] \hat k \text{When the particle is moving from C to D} \\ (3)\overrightarrow {L} = mv \bigg[\large\frac{R}{\sqrt 2} \normalsize a \bigg] \hat k \text{When the particle is moving from B to C} \\ (4)\overrightarrow {L} = \large\frac{mv}{\sqrt 2} \normalsize R \hat k \text{When the particle is moving from D to A}\end{array} $