Question

A horizontal plane supports a fixed vertical cylinder of radius $R$ and a particle is attached to the cylinder by a horizontal thread $AB$ as shown in figure. A horizontal velocity $v_0$ is imparted to the particle, normal to the thread, then during subsequent motion:

• A. Angular momentum of particle about $O$ remains constant.
• B. Angular momentum of particle about $B$ remains constant.
• C. Momentum of particle remains constant.
• D. Kinetic energy of particle remains constant.

Answer 1

The correct option is A Angular momentum of particle about $O$ remains constant.

Since there is no external torque acting on the particle, it's angular momentum about the axis of rotation is constant. The particle's axis of rotation passes through point O.
Kinetic energy does not remain constant because, according to the conservation of angular momentum, it's velocity increases as it's radius decreases while it rotates around the cylinder.
Answer: A