Question

Two spheres of mass $2\text{kg}$ and $6\text{kg}$ are moving with velocities $4\text{m/s}$ and $8\text{m/s}$ away from each other along the same line. The ball of mass $2\text{kg}$ is moving towards left. The velocity of the center of mass is

• A. $4\text{m/s}$
• B. $7\text{m/s}$
• C. $5\text{m/s}$
• D. $3\text{m/s}$

Answer 1

The correct option is C $5\text{m/s}$

Given, mass $m_1=2\text{kg}$ & $m_2=6\text{kg}$
Taking left to be negative direction.
Velocity of masses, $v_1=-4\text{m/s}$
& $v_2=8\text{m/s}$

Thus, we have velocity of center of mass
$V_{cm}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}=\frac{2(-4)+6\left(8\right)}{2+6}=\frac{40}{8}=5\text{m/s}$