Question

Two objects of masses 200 gm and 500 gm possess velocities $10\overrightarrow{i}m/s$ and $3\overset{\land}{i} + 5\overset{\land}{j}$ m/s respectively. The velocity of their centre of mass in m/s is :

• A. $5\overset{\land}{i} - 25\overset{\land}{j}$
• B. $\frac{5}{7}\overset{\land}{i} - 25\overset{\land}{j}$
• C. $5\overset{\land}{i} + \frac{25}{7}\overset{\land}{j}$
• D. $25\overset{\land}{i} - \frac{5}{7}\overset{\land}{j}$

Answer 1

Answer: (C)

$5\overset{\land}{i} + \frac{25}{7}\overset{\land}{j}$

Answer 2

$v_{cm}^{\rightarrow} = \frac{m_{1}{\overrightarrow{v}}_{1} + m_{2}{\overrightarrow{v}}_{2}}{m_{1} + m_{2}} = \frac{200 \times 10\widehat{i} + 500 \times (3\widehat{i} + 5\widehat{j})}{200 + 500}$

$v_{cm}^{\rightarrow} = 5\widehat{i} + \frac{25}{7}\widehat{j}$