A small ball of mass `1 kg` is kept in circular path of radius `1 m` Inside a concentric smooth horizontal fixed casing of radius `R`. Angular speed of the ball in the circular motion is `1 rads^(-1)`. At a certain moment the string, which kept the ball in the circular path breaks and the ball goes off tangentially to the wall of rigid casing and bounces off elastically and again hits the casing and bounces off. This way, the ball traces a regular hexagon. Consider all the collisions to be elastic.

Following quantities of the ball will remain a constant before and after any collision

Options

A. linear momentum
B. kinetic energy, angular momentum about the centre of the circle
C. velocity, angular momentum about the centre of the circle, kinetic energy
D. none of these

Answer

B

Explanation

Since an impulse acts on the ball during each collision, so linear momentum does not remain constant.
The impulsive force is directed towards the centre of hexagon, therefore the lever arm of this imupulsive force is zero.
As are result, it does not produce any torque and angular momentum remains costant. Further, kinetic energy also remains same for elastic collision.