Question

Two spheres made of same material have radii r and 2r. They are initially touching each other and start moving out along the line joining their centres with velocities 4v and v respectively. The velocity of their centre of mass is

• A. zero
• B. 4v/9 in the direction of motion of larger sphere
• C. 4v/9 in the direction of motion of smaller sphere
• D. 4v/3 in the direction of motion of larger sphere

Answer 1

The correct option is B

4v/9 in the direction of motion of larger sphere

$V_{cm}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}\Rightarrow V_{cm}=\frac{\rho \frac{4}{3}\pi r^3\left(4v\right)+\rho \frac{4}{3}\pi \left(2r{)}^3\right(v)}{\rho \frac{4}{3}\pi r^3+\rho \frac{4}{3}\pi (2r{)}^3}$

= $\frac{\frac{4}{3}\pi r^3(-4v+8v)}{\frac{4}{3}\pi r^3(1+8)}$

${\overrightarrow{v}}_{cm}=\frac{4v}{9}towardslargersphere$