Q. Two objects of masses $200g$ and $500g$ possess velocities $10\widehat{i}\ m/s$ and $3\widehat{i} + 5\widehat{j}\ m/s$ respectively. The velocity of their centre of mass in $m/s$ is
A) $5\widehat{i} - 25\widehat{j}$
B) $\frac{5}{7}\widehat{i} - 25\widehat{j}$
C) $5\widehat{i} + \frac{25}{7}\widehat{j}$
D) $25\widehat{i} - \frac{5}{7}\widehat{j}$
Explanation
(c) ${\overrightarrow{v}}_{cm} = \frac{m_{1}{\overrightarrow{v}}_{1} + m_{2}{\overrightarrow{v}}_{2}}{m_{1} + m_{2}} = \frac{200 \times 10\widehat{i} + 500 \times (3\widehat{i} + 5\widehat{j})}{200 + 500}$
${\overrightarrow{v}}_{cm} = 5\widehat{i} + \frac{25}{7}\widehat{j}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.