Question

A $20kg$of ball moving with a velocity $6m{s}^{-1}$collides with a $30kg$of ball initially at rest. If both of them coalesce, then the final velocity of the combined mass is

• A. $6m{s}^{-1}$
• B. $5m{s}^{-1}$
• C. $3.6m{s}^{-1}$
• D. $2.4m{s}^{-1}$
• E. $1.2m{s}^{-1}$

Answer 1

The correct option is D

$2.4m{s}^{-1}$

Step 1: Given data and drawing the diagram of situation

Mass of the first ball, $m_1=20kg$

Mass of the second ball, $m_2=30kg$

Initial velocity of first ball, $u_1=6m{s}^{-1}$

Initial velocity of the second ball, $u_2=0m{s}^{-1}$

Step 2: Find the final velocity of the combined mass

Apply the conservation of momentum since no external force is acting,

$$\begin{gathered} m_1{u}_1+m_2{u}_2=\left(m_1+m_2\right)v \\ 20\times 6+30\times 0=(20+30)v \\ 120+0=50v \\ v=2.4m{s}^{-1} \end{gathered}$$

Hence, option (D) is correct.