Three particles of masses 20 , g,30 , g,and 5 | vedclass

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(A) The velocity of the center of mass $\vec{v}_{cm}$ is given by the formula: $\vec{v}_{cm} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2 + m_3 \vec{v}_3}{m_

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

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

Three particles of masses $20 \, g$,$30 \, g$,and $50 \, g$ have velocities $10 \, \hat{i}$,$10 \, \hat{j}$,and $10 \, \hat{k}$ respectively. The velocity of the center of mass of these three particles is:

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