According to the question, Given, mass of the particle =m
∴ Linear momentum of the particle, p=mv or =mv
^
i
Position of particle at time t,r=x
^
i
+y
^
j
=vt
^
i
+y
^
j
‌‌‌‌(∵x=vt) ∴ Angular momentum of the particle about O. L=r×p=(vt
^
i
+y
^
j
)×mv
^
i
L=|
^
i
^
j
^
k
vt
y
0
v
0
0
| L=
^
i
(0−0)−
^
j
(0−0)+
^
k
(0−vy) =−vy
^
k
( constant ) (∵ Particle is moving in +ve x -direction.) Hence, angular momentum of particle w.r.t the origin remains constant for all positions of the particle.