The correct option is
C →LO remains constant while
→LP varies with time.
Angular momentim about
O :
As we know, angular momentum
→L=m(→r×→V) Here
→r=−−→OA. Since mass is undergoing circular motion,
→V will be in the tangential direction of a circle in the plane of circular motion.
→LO=m(−−→OA×→V) Angular momentum will be in z-direction (perpendicular to the plane of circular motion).
After some time, mass is at
B. Velocity will be in tangential direction. Hence
→LO=m(−−→OB×→V) has the same magnitude and direction.
i.e
→LO remains constant.
Angular momentum about point
P :
Here,
→r=−−→PA and angular momentum will be
→L=m(−−→PA×→V) →V will be in tangential direction in the circular plane. Hence, the direction of angular momentum will be as shown in figure. (by right hand thumb rule).
![](https://search-static.byjusweb.com/question-images/byjus/ckeditor_assets/pictures/927669/original_2.png)
After time
t, when particle is at
B,
→r=−−→PB and velocity vector will be in tangential direction.
So, angular momentum
→L=m(−−→OB×→V) and the direction of angular momentum (from right hand rule ) as shown in the figure.
Hence, magnitude of angular momentum will be same about point
P, but direction is changing.
∴ Angular momentum about point
O is constant, but about point
P it is varying.