A body of mass m1 , moving with velocity u1 collides head  on with a body of mass m2 moving with a velocity u2 the two bodies stick together after the collision the loss of kinetic energy after the collision is ?

Ans) Initial KE of the system= 1/2 [ m1.u1^2  +  m2.u2^2 ]
applying conservation of momentum we get new velocity of the new body=  (m1.u1-m2.u2) / (m1+m2)
new KE of the Body=      [  (m1.u.1 - m2.u2) / 2.(m1+m2)   ]^2
Subtracting and simplyfing we get the loss in KE after Collision=  [ m1.m2. (u1 + u2)^2 ] / [ 2.(m1 + m2) ]