A ball of mass $100g$ moving at a speed of $12m{s}^{-1}$ strikes another ball of mass $200g$ at rest. After the collision both the balls move with common velocity. Find the common velocity.

Step 1: Given data

First ball of mass, $m_1=100g$

Initial velocity of the first ball, $u_1=12m{s}^{-1}$

Second ball of mass, $m_2=200g$

Initial velocity of second ball, $u_2=0$

the question states that after the collision, both the ball moves with common velocity.

Therefore, the final velocity ‘$v$’ of both the balls are same, Hence $v_1=v_2$

Step 2: Finding the common velocity

According to law of conservation of momentum, we know that momentum remains conserved before and after collision for an isolated system.

Therefore, $m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

Here, $v_1=v_2=v$

Therefore, $m_1{u}_1+m_2{u}_2=m_{1}v+m_{2}v$

$$\begin{gathered} 100\times 12+0=100\times v+200\times v \\ 1200=300v\Rightarrow v=\frac{1200}{300}=4m{s}^{-1} \end{gathered}$$

Thus, the common velocity is $4m{s}^{-1}$