A bomb of mass 3.0 ~kg explodes in air into two pieces of masses 2.0 ~kg and 1.0 ~kg . The smaller mass goes at a speed of 80 ~m / s . The total energy imparted to the two fragments is

Step-by-step solution

Velocity of second piece can be find out using conservation of momentum. aligned & O =m₁ v₁+m₂ v₂=2 v₁+1 80 & v₁=-40 ~m / s . aligned Negative sign showing that particle is moving in opposite direction of other particle direction. Energy imparted to the fragments are converted into their kinetic energy. aligned Total energy & = 1 2 m₁ v₁^2+ 1 2 m₂ v₂^2 & = 1 2 2 1600+ 1 2 1 6400 & =4800 ~J =4.8 ~kJ . aligned