Question

Two bodies of masses $10\text{kg}$ and $2\text{kg}$ are moving with velocities $2\hat{i}-7\hat{j}+3\hat{k}$ and $-10\hat{i}+35\hat{j}-3\hat{k}\text{m/s}$ respectively. The velocity of their centre of mass is

• A. $2\hat{i}\text{m/s}$
• B. $2\hat{k}\text{m/s}$
• C. $(2\hat{j}+2\hat{k})\text{m/s}$
• D. $(2\hat{i}+2\hat{j}+2\hat{k})\text{m/s}$

Answer 1

The correct option is B $2\hat{k}\text{m/s}$

$m_1=10\text{kg},m_2=2\text{kg}$
$\overrightarrow{v_i}=2\hat{i}-7\hat{j}+3\hat{k}$ and $\overrightarrow{v_2}=-10\hat{i}+35\hat{j}-3\hat{k}$
$\therefore {\overrightarrow{v}}_{CM}=\frac{m_1\overrightarrow{v_1}+m_2\overrightarrow{v_2}}{m_1+m_2}$
${\overrightarrow{v}}_{CM}=\frac{10(2\hat{i}-7\hat{j}+3\hat{k})+2(-10\hat{i}+35\hat{j}-3\hat{k})}{10+2}$
${\overrightarrow{v}}_{CM}=2\hat{k}\text{m/s}$
Hence, the correct answer is option (b).