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 

Options

A. `(1 - e)/(1 +e)`
B. `(1 + e)/(1 - e)`
C. `(1 + e)/(2)`
D. `(1 - e)/(2)`

Answer

C

Explanation

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)`.