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 Fig. The particle initially rest on a horizontal plane. A horizontal velocity `v_(0)` is imparted to the particle, normal to the threading during subsequent motion. Point out the false statements:

Options

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

A, B, C, D

Explanation

Weight of the particle is balanced by the normal reaction of the floor. Hence, the resultant force action on the particle is provided by the tension in the thread.
The line of action of this tension passes through `'B'` at the initial moment only. After that it does not pass through `'B'`. Hence, the tension produces a moment angular momentum about `B` does not momentum about `B`. It means, conserved. The tension always produces a moment about `O`. Magnitude of this moment is equal to `TR` in an anticlockwise direction. Hence, options (a), (b) and (c) are incorrect. Since neither external work is done on the particle or energy is lost against friction, therefore `KR` of the ball remains constant. Hence, option (d) is correct