A point mass is tied to one end of a cord, other end of which passes through a hollow tube caught in one hand. The point mass is being revolved in a horizontal circle of radius $r_1$ with a velocity $u$. The cord is then pulled down so that the radius of the circle reduces to $r_2$.
Now, my teacher said that to find the final velocity (say $v$) at radius $r_2$ we can use conservation of angular momentum about center of circle.
But, I do not think that is correct as torque due to gravity ($mgr$) is acting on the point mass. So we should not be able to use conservation of angular momentum. Please tell me if I am going wrong somewhere. Can we conserve angular momentum or not? And why so ?