A ball collides impinges directly on a similar ball at rest. The first ball is brought to rest after the impact. If half of the kinetic energy is lost by impact, the value of coefficient of restitution (e) is

∴ Initial KE, Ki = 12mu12+12mu22 = 12mu21and final KE, Kf = 12mv21+12mv22 = 12mv22Loss in KE, ∆K = Ki-kf  = 12mu21-12mu22It is given 12(12mu21) = 12mu21-12mv22(∴ Half of its KE is lost by impact)or u21 = 2v22 or v2 = u12Hence, coefficient of restitution, e = |v2-v1u1-u2| = v2u1 = 12