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Question

A bomb of mass 16kg at rest, explodes into two pieces of masses 4kg and 12kg. After explosion, the velocity of the 12 kg mass is 4 m/s. What is the velocity of the 4 kg piece?


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Solution

Step 1: Given data

  1. The mass of the bomb is 16kg.
  2. The mass of the first piece is 4kg.
  3. The mass of the second piece is m1=12kg and its velocity is v2=4m/s.
  4. If a bomb of mass M explodes into two pieces of mass m1 and m2 with velocities v1 and v2,
  5. Then from the concept of conservation of linear momentum, we know that the linear momentum of a system of particles remains constant in absence of external force, i.e, MV=m1v1+m2v2, where V is the velocity of the bomb.

Diagram

A bomb of mass 16 kg at rest explodes into two pieces of mas

Step 2: Find the velocity of the second piece

Let, m1 and m2 are the mass of the two pieces with velocities v1 and v2,

From the principle of conservation of linear momentum,

MV=m1v1+m2v2

0=+4×v1+12×4orv1=-484=-12.orv1=-12m/s.

Neglecting the minus sign of velocity, because the two masses are moving in opposite directions from each other.

So, the velocity of the first body is 12m/s.


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