Question

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

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

Answer 1

The correct option is C $5\hat{i}+\frac{25}{7}\hat{j}$

Velocity of center of mass is given by:

$\overrightarrow{V}=\frac{\sum m_i{\overrightarrow{v}}_i}{\sum m_i}=\frac{m_1{\overrightarrow{v}}_1+m_2{\overrightarrow{v}}_2}{m_1+m_2}\overrightarrow{V}=\frac{0.2\left(10\hat{i}\right)+0.5(3\hat{i}+5\hat{j})}{0.2+0.5}=\frac{2\hat{i}+1.5\hat{i}+2.5\hat{j}}{0.7}=5\hat{i}+\frac{25}{7}\hat{j}$