Question

Two spheres of masses $4kg$ and $8kg$ are moving with velocities $2{ms}^{-1}$ and $3{ms}^{-1}$ away from each other along the same line. The velocity of centre of mass is

• A. $\frac{8}{3}{ms}^{-1}$ towards second sphere
• B. $\frac{8}{3}{ms}^{-1}$ towards first sphere
• C. $\frac{4}{3}{ms}^{-1}$ towards second sphere
• D. $\frac{4}{3}{ms}^{-1}$ towards first sphere

Answer 1

The correct option is C $\frac{4}{3}{ms}^{-1}$ towards second sphere

Away from each other so $opposite$ velocities.

Now taking $second$ sphere as $positive$ velocity,

we have $V_{cm}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}=\frac{4(-2)+8\left(3\right)}{4+8}=\frac{4}{3}m/s$ positive so towards the second sphere.