# Two bodies of 6kg and 4 kg masses have their velocity $5\hat{i} – 2\hat{j} + 10 \hat{k}$ and $10\hat{i} – 2\hat{j} + 5 \hat{k}$ respectively.

Q: Two bodies of 6kg and 4 kg masses have their velocity $5\hat{i} – 2\hat{j} + 10 \hat{k}$ and $10\hat{i} – 2\hat{j} + 5 \hat{k}$ respectively. Then, the velocity of their centre of mass is

Sol: The velocity of centre of mass is

$\large \vec{v_{cm}} = \frac{m_1 \vec{v_1} + m_2 \vec{v_2}}{m_1 + m_2}$

$\large \vec{v_{cm}} = \frac{6 ((5\hat{i} – 2\hat{j} + 10 \hat{k})) + 4 (10\hat{i} – 2\hat{j} + 5 \hat{k})}{6 + 4}$

$\large = 7 \hat{i} – 2\hat{j} + 8\hat{k}$