in this question
we have taken the angular momentum about the point c but we can
see that there has been a torque acting during the collision
which tends to rotate the body of mass M . this
could have been true when we have taken any point in the line of
momentum of mass m because then the toque about that point
is 0 as the line of force passes through it . But as shown in
figure we have taken the point C to observe the angular momentum
because the toque is acting about the point C
You can conserve angular momentum of rod + particle about any fixed pt in space
Is it true that this could only possible of we consider particle
to be in our system then force during collision becomes internal
and then torque becomes zero and angular momentum can be
conserved then only
here it is so. But there can be a case where the net force may be
non zero, but still angular momentum canbe conserved
But then that force may produce some net torque so how angular momentum conservation can be applied
It may be possible in certain cases where force may acting on the system but we can conserve angular momentum about the point of the application of force about which there won't be any torque