JEE Main · 2016 · 03 Apr 2016 · Offline · Rotational Mechanics

Angular momentum about the origin is $\vec{L}=m\vec{r}\times \vec{v}$, and on each straight leg its magnitude is $mv$ times the perpendicular distance from the origin to that line of motion, with the sign set by the sense of rotation. Working leg by leg with the geometry of the square, the segment from C to D gives $\vec{L}=mv\left[\frac{R}{\sqrt{2}}+a\right]\hat{k}$. The statement that assigns this leg the value $mv\left[\frac{R}{\sqrt{2}}-a\right]\hat{k}$ disagrees with the correct perpendicular distance, so it is the false one.