Question

If a body in rest breaks up into two pieces of equal masses, then, the parts will

Answer 1

Step 1: List the known values and conditions

Let the velocities of the first piece be $v_1$ and the second piece be $v_2$.

It is given that the mass of both the pieces will be equal.

$\therefore m_1=m_2=m$

Since the body is at rest, the initial velocity of the body $v=0$

Step 2: Explain using momentum conservation

According to the conservation of linear momentum,

$$\begin{gathered} \mathrm{Net}\mathrm{final}\mathrm{momentum}=\mathrm{Net}\mathrm{Initial}\mathrm{momentum} \\ {m}_1{v}_1+m_2{v}_2=\left(m_1+m_2\right)v \end{gathered}$$

Upon substituting the values we get,

$$\begin{gathered} m{v}_1+m{v}_2=\left(m+m\right)\left(0\right) \\ or \\ m\left(v_1+v_2\right)=0 \end{gathered}$$

$\Rightarrow v_1+v_2=0$

$\Rightarrow$ $v_1=-v_2$

Here, the negative sign indicates the motion of both the pieces in opposite direction.

Hence, the two pieces of equal masses start to move in opposite directions.