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 the figure. The particle initially rest on horizontal plane. A horizontal velocity $v_0$ is imparted to the particle, normal to the threading during subsequent motion. Point out the false statements:

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

Answer 1

Answer: (A), (B), (C)

The correct options are
A Momentum and kinetic energy both remain constant
B Angular momentum of particle about $O$ remains constant
C Angular momentum about $B$ remains constant

Since torque about point O due to force by string is non zero (as angle between OA and AB is non zero), angular momentum is not constant.(Since $\Gamma =\frac{dL}{dt}$)

Same reason as part 1. Since angle between force by string and AB will vary from 0 as particle will move.

Since velocity of particle is continuously changing, direction of momentum is changing and hence momentum is not constant.

Since work done by the string force is zero as velocity is perpendicular to force, change in kinetic energy is 0 and hence kinetic energy remains constant.