Answer
a) stays the same
b) III
Work Step by Step
(a) We know that when the student drops the weight, no torque is produced; the angular momentum of the student-piano stool system remains the same and hence the student's angular speed does not change.
(b) We know that the correct option is (III) -- that is, dropping the weights exerts no torque on the student, but the floor exerts a torque on the weights when they land.
