Find coefficient of restitution

Let A & B be two balls

$UA=u , VA=0\space\space \&\space\space UB=0 , VB=v $

Applying coefficient of restitution eqn,

$e = - (VB - VA)/( uB - uA) = - (v) /(-u) = v/u\text {____(i)} $

Now, initial kinetic energy $= (1/2)mu2 $

Final kinetic energy $= (1/2)mv2 $

But as half the kinetic energy is lost, initial KE= 2* final KE

$(1/2)mu2 = 2* (1/2)mv2 \\ v/u = 1/\sqrt2\text {_____(ii) } $

from (i) & (ii)

$e = 1/\sqrt2 = 0.707 $

Coefficient of restitution is $0.707 $