Question

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

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

Answer 1

The correct option is B $2\hat{k}m{s}^{-1}$

$V_{cm}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}=\frac{10(2\hat{i}-7\hat{j}+3\hat{k})+2(-10\hat{i}+35\hat{j}-3\hat{k})}{10+2}=\frac{20\hat{i}-70\hat{j}+30\hat{k}-2\hat{i}+70\hat{j}-6\hat{k}}{12}=\frac{0\hat{i}+0\hat{k}+24\hat{k}}{12}=2\hat{k}m/s$