A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinctic energy is lost by impact, the value of coefficient of restitution is

A ball impinges directly on a similar ball at rest. The first ball is

1.	A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinctic energy is lost by impact, the value of coefficient of restitution is
Answer» `1/(2sqrt(2))` `1/(sqrt3)` `1/(sqrt2)` `(sqrt3)/(2)` Solution :LET `u_1` and `v_1` be the initial and FINAL velocities for ball 1 and `u_2` and `v_2` be the final velocities for ball 2. Here, `u_2 = 0 and v_1 = 0` `K_i = 1/2 m u_1^2 + 1/ m u_2^2 = 1/2 m u_1^2` `K_f = 1/2 mv_1^2 + 1/2 mv_2^2 = 1/2 mv_2^2` Loss of K.E. = `1/2 m u_1^2 - 1/2 m v_2^2` According to questions, `1/2 (1/2 m u_1^2) = 1/2 m u_1^2 - 1/2 mv_2^2` (as half of KE is LOST be IMPACT) `:. u_1^2 = 2v_2^2 " or " v_2 = (u_1)/(sqrt2) :.e = (v_2 - v_1)/(u_1 - u_2) = (v_2)/(u_1) = 1/(sqrt2)`.