STATEMENT - 1 : Two identical balls B and C lie on a horizontal smooth straight groove so that they are touching. A third identical ball A moves at a speed v along the groove. And collides with B as shown in figure. If the collisions are perfectly elastic, then after the collision, balls A and B will come to rest and ball C moves with velocity v to the right.
because

STATEMENT - 2 : In an elastic collision, linear momentum and kinetic energy are both conserved.

Options

A. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1.
B. Statement - 1 is True, Statement - 2 is True, Statement - 2 is NOT a correct explanation for statement - 1.
C. Statement - 1 is True, Statement - 2 is False.
D. Statement - 1 is False, Statement - 2 is True.

Answer

A

Explanation

Linear momentum will be conserved if A comes to rest and B & C moves to the right with a velocity v/2 each or, A, B and C all move to the right with velocity v/3 each. It is easy to see that in these two cases, the kinetic energy is not conserved. Hence the only result of the collision is the one given in statenet 1. Hence (A) is correct.