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?

Answer 1

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 $m_1=12kg$ and its velocity is $v_2=4m/s.$
4. If a bomb of mass $M$ explodes into two pieces of mass $m_1$ and $m_2$ with velocities $v_1$ and $v_2$,
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, $MV=m_1{v}_1+m_2{v}_2$, where $V$ is the velocity of the bomb.

Diagram

Step 2: Find the velocity of the second piece

Let, $m_1$ and $m_2$ are the mass of the two pieces with velocities $v_1$ and $v_2$,

From the principle of conservation of linear momentum,

$MV=m_1{v}_1+m_2{v}_2$

$$\begin{gathered} 0=+\left(4\times v_1\right)+\left(12\times 4\right) \\ or{v}_1=-\frac{48}{4}=-12. \\ or{v}_1=-12m/s. \end{gathered}$$

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 $12m/s$.