Question

An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down are:

• (A) Angular velocity and total kinetic energy
• (B) Total angular momentum and total energy
• (C) Angular velocity and moment of inertia about the axis of rotation
• (D) Angular velocity and moment of inertia about the axis of rotation

Answer 1

The Correct Option is B

Explanation:
The forces acting on the beads are conservative forces. So the total energy.Kinetic energy + potential energy will remain constant.When the beads are sliding down, no external torque acts on them. Therefore, according to the law of conservation of angular momentum, the total angular momentum of the system remains constant:$I\omega =\text{constant}$The angular velocities of the beads will not remain constant as angular velocity will change with a change in the moment of inertia.As the distance of the beads from the line of axis AO is changing, the moment of inertia of the system also changes.From the above discussion, it is clear that the total angular momentum and total energy of the system only remain constant.Hence, the correct option is (B).