Astar of uniform mass with a radius r rotates about its diameter with angular momentum l. under the action of internal forces the star collapses until its radius is one fourth of its initial size. the magnitude of its new angular momentum is:
l
16l
l/16
4l
l/4

L / 16

Explanation:

Mass = m, Radius = R, angular momentum = L

Now, new radius, R' = R/4, mass = m, angular momentum, L' = ?

By the law of conservation of angular momentum

If there is no external torque is applied, the angular momentum of the system remains conserved.

L = I x w

Moment of inertia I depends on the mass and the square of radius of the star.

If the radius is one fourth, the angular momentum becomes one sixteenth.

So, L' = L / 16