Answer
$\frac{mVa}{6}$
Work Step by Step
Please see the attached image first.
Here we use the equation, Angular momentum $(L)=I\omega$
$L=I\omega-(1)$
We know for a thin rod, the rotational inertia of a perpendicular axis through its center of mass $(I)=\frac{1}{12}ma^{2}-(2)$
Also, we can write,
$V=r\omega$
$V=\frac{a}{2}\omega=\gt \omega=\frac{2V}{a}-(3)$
$(2),(3)=\gt (1)$
$L=\frac{1}{12}ma^{2}\times 2V=\frac{mVa}{6}$
