Question

A bomb of mass 20 kg at rest explodes in air into two pieces of masses 4 kg and 16kg.The velocity of the 16 kg mass is 4m/sec then the kinetic energy of other mass is

Answer 1

According to law of conservation of momentum:

Total initial momentum = Total final momentum

m₁u₁+m₂u₂=m₁v₁+m₂v₂

As the entire system (bomb) is at rest:

Total initial momentum =  0

After explosion, the fragments move in opposite directions; due to which velocity of fragments take upon positive and negative value-

So, m₁v₁ = m₂v₂: By substituting given values ( m₁ = 4kg, m₂ = 16kg, v₂=4m/s)-

4(v₂) = 16(4) → v₂ = 16m/s

Kinetic energy = 1/2(m)(v)²

Here, kinetic energy would be (answer) = 1/2(m₁)(v₁)²:

1/2(4)(16)² = 2(256) = 512 Joules