The velocities of three particles of masses 2 | vedclass

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(A) Given masses: $m_1 = 20 \ g$,$m_2 = 30 \ g$,$m_3 = 50 \ g$. Velocities: $\vec{v}_1 = 10 \hat{i} \ m/s$,$\vec{v}_2 = 10 \hat{j} \ m/s$,$\vec{v}_3 =

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$2 \hat{i} + 3 \hat{j} + 5 \hat{k}$

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(A) Given masses: $m_1 = 20 \ g$,$m_2 = 30 \ g$,$m_3 = 50 \ g$. Velocities: $\vec{v}_1 = 10 \hat{i} \ m/s$,$\vec{v}_2 = 10 \hat{j} \ m/s$,$\vec{v}_3 = 10 \hat{k} \ m/s$. The velocity of the centre of mass is given by: $\vec{v}_{cm} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2 + m_3 \vec{v}_3}{m_1 + m_2 + m_3}$ Substituting the values: $\vec{v}_{cm} = \frac{20(10 \hat{i}) + 30(10 \hat{j}) + 50(10 \hat{k})}{20 + 30 + 50}$ $\vec{v}_{cm} = \frac{200 \hat{i} + 300 \hat{j} + 500 \hat{k}}{100}$ $\vec{v}_{cm} = 2 \hat{i} + 3 \hat{j} + 5 \hat{k}$

The velocities of three particles of masses $20 \ g$,$30 \ g$ and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$ and $10 \hat{k}$,respectively. The velocity of the centre of mass of the three particles is

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