Question

A shell of mass $m$ moving with velocity $V$ suddenly breaks into 2 pieces. The part having mass $\frac{m}{4}$ remains stationary. The velocity of the other shell will be:

Answer 1

Step 1: Given data

1. The mass of the body is $m$
2. The mass of the two broken parts after the explosion is $\frac{m}{4}$ and $\left(m-\frac{m}{4}\right)$.
3. The velocity of the body is $V$.
4. The velocity of the first piece of mass $\frac{m}{4}$ is $v_1=0$.

Step 2: Formula used

1. The linear momentum of a body is the product of the mass and velocity of the body, i.e, linear momentum, $P=mv$, where, m and v are the mass and velocity of a body.
2. We know in an explosion the linear momentum is conserved. So, $MV=m_1{v}_1+m_2{v}_2$, where, M and V are the mass of the body, $m_1,m_2$ and $v_1,v_2$ are the masses and velocities of the broken pieces.

Step 3: Finding the velocity of the second piece

Let, $v_2$ be the velocity of the second piece.

According to the conservation of linear momentum, $MV=m_1{v}_1+m_2{v}_2$

So,

$$\begin{gathered} mv=\left(\frac{m}{4}\times 0\right)+\left(m-\frac{m}{4}\right)v_2\left(Since,v_1=0\right). \\ ormv=\frac{3m}{4}\times v_2 \\ or{v}_2=\frac{4mv}{3m}=\frac{4}{3}v \\ or{v}_2=\frac{4}{3}v. \end{gathered}$$

Therefore, the velocity of the second piece is $\frac{4}{3}v$.