Question

Two bodies of masses 10 kg and 2 kg are moving with velocities $2\hat{i}-7\hat{k}+3\hat{j}m{s}^{-1}$ and $-10\hat{i}+35\hat{k}-3\hat{j}m{s}^{-1}$ respectively. The velocity of their centre of mass is

• A. $2\hat{i}m{s}^{-1}$
• B. $2\hat{j}m{s}^{-1}$
• C. $(2\hat{j}+2\hat{k})m{s}^{-1}$
• D. $(2\hat{i}+2\hat{j}+2\hat{k})m{s}^{-1}$

Answer 1

Answer: (B)

$2\hat{j}m{s}^{-1}$

$m_1=10kg\overrightarrow{v_1}=2\hat{i}-7\hat{k}+3\hat{j}m/s$

$m_2=2kg\overrightarrow{v_2}=-10\hat{i}+35\hat{k}-3\hat{j}m/s$

velocity of centre of mass should be

$\overrightarrow{v}=\frac{m_1\overrightarrow{v_1}+m_2\overrightarrow{v_2}}{m_1+m_2}$

or $\overrightarrow{v}=\frac{20\hat{i}-70\hat{k}+30\hat{j}+(-20\hat{i}+70\hat{k}-6\hat{j})}{10+2}$

$\Rightarrow \overrightarrow{v}=\frac{24\hat{j}}{12}=2\hat{j}m/s$