The velocities of three particles of masses 2 | vedclass

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(A) The velocity of the centre of mass is given by the formula: $v_{cm} = \frac{m_1 v_1 + m_2 v_2 + m_3 v_3}{m_1 + m_2 + m_3}$ Given: $m_1 = 20 \ g, v

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

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(A) The velocity of the centre of mass is given by the formula: $v_{cm} = \frac{m_1 v_1 + m_2 v_2 + m_3 v_3}{m_1 + m_2 + m_3}$ Given: $m_1 = 20 \ g, v_1 = 10 \hat{i}$ $m_2 = 30 \ g, v_2 = 10 \hat{j}$ $m_3 = 50 \ g, v_3 = 10 \hat{k}$ Total mass $M = 20 + 30 + 50 = 100 \ g$ Substituting the values: $v_{cm} = \frac{(20 	imes 10 \hat{i}) + (30 	imes 10 \hat{j}) + (50 	imes 10 \hat{k})}{100}$ $v_{cm} = \frac{200 \hat{i} + 300 \hat{j} + 500 \hat{k}}{100}$ $v_{cm} = 2 \hat{i} + 3 \hat{j} + 5 \hat{k}$

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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