A metal ball of mass 2 ~kg moving with a speed of 10 ~ms ⁻¹ had a head-on collision with a stationary ball of mass 3 ~kg . If after collision, both the balls move together, then the loss in kinetic energy due to collision is

Step-by-step solution

Apply conservation of momentum, array l m ₁ v ₁= ( m ₁+ m ₂ ) v v = m ₁ v ₁ ( ~m ₁+ m ₂ ) array Here v ₁=36 ~km / hr =10 ~m / s , array l m ₁=2 ~kg , ~m ₂=3 ~kg v = 10 2 5 =4 ~m / s array K.E. (initial) = 1 2 2 (10)²=100 ~J K.E. (Final) = 1 2 (3+2) (4)²=40 ~J Loss in K.E. =100-40=60 ~J Alternatively use the formula - E _ k = 1 2 m ₁ ~m ₂ ( ~m ₁+ m ₂ ) ( u ₁- u ₂ )²