The first ball of mass m moving with a velocity u collides head on with the second ball of mass m at rest. If the coefficient of restitution is e, the ratio of final velocity of the second ball to the initial velocity of the first ball is

The first ball of mass m moving with a velocity u collides head on wit

1.	The first ball of mass m moving with a velocity u collides head on with the second ball of mass m at rest. If the coefficient of restitution is e, the ratio of final velocity of the second ball to the initial velocity of the first ball is
Answer» `(1 - E)/(1 +e)` `(1 + e)/(1 - e)` `(1 + e)/(2)` `(1 - e)/(2)` SOLUTION :According to conservation of linear MOMENTUM, we get `m u + 0 = mv_1 + mv_2` or `u = v_1 + v_2"" ………(i)` COEFFICIENT of restitution, `e = (v_2 - v_1)/(u_1 - u_2) ` But `u_1 - u_2 = u "" ( :. u_2 = 0)` `:. e = (v_2 - v_1)/(u)` or `eu = v_2 - v_1 "" .....(ii)` Addition equations (i) and (ii), we get `u (e + 1) = 2 v_2 " or " v_2 = (u(e + 1))/(2)` `:. ("Final VELOCITY of " 2^(nd) "ball")/("Initial velocity of " 1^(st) " ball) = (v_2)/u = (e + 1)/(2)`.