Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are $$v$$ and 2$$v$$, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60$$^\circ$$ to 30$$^\circ$$ at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10 m/s$$^2$$).

If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is

Statement 1 :

In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Statement 2 :

In an elastic collision, the linear momentum of the system is conserved.