A bomb of mass 18 ~kg at rest explodes into two pieces of masses 6 ~kg and 12 ~kg . The velocity of 12 ~kg mass is 4 ~m / s . The kinetic energy of the other mass is

Step-by-step solution

Mass of bomb, M=18 ~kg Mass of pieces, m₁=6 ~kg , m₂=12 ~kg Velocity of 12 ~kg mass, v₂=4 ~m / s Let v₁ be the velocity of 6 ~kg mass. According to conservation of linear momentum, aligned M 0 &=m₁ v₁+m₂ v₂ m₁ v₁ &=-m₂ v₂ 6 v₁ &=-12 4 v₁ &=-8 ~m / s Kinetic energy of other (6 ~kg ) mass, K &= 1 2 m₁ v₁² &= 1 2 6 (-8)²=3 64=192 ~J aligned