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(C) Given masses are $m_1 = 200 \ gm = 0.2 \ kg$ and $m_2 = 500 \ gm = 0.5 \ kg$. Velocities are $\vec{v}_1 = 10 \hat{i} \ m/s$ and $\vec{v}_2 = (3 \h

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$5 \hat{i} + \frac{25}{7} \hat{j}$

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(C) Given masses are $m_1 = 200 \ gm = 0.2 \ kg$ and $m_2 = 500 \ gm = 0.5 \ kg$. Velocities are $\vec{v}_1 = 10 \hat{i} \ m/s$ and $\vec{v}_2 = (3 \hat{i} + 5 \hat{j}) \ m/s$. The velocity of the centre of mass $\vec{v}_{cm}$ is given by the formula: $\vec{v}_{cm} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2}{m_1 + m_2}$ Substituting the values: $\vec{v}_{cm} = \frac{0.2(10 \hat{i}) + 0.5(3 \hat{i} + 5 \hat{j})}{0.2 + 0.5}$ $\vec{v}_{cm} = \frac{2 \hat{i} + 1.5 \hat{i} + 2.5 \hat{j}}{0.7}$ $\vec{v}_{cm} = \frac{3.5 \hat{i} + 2.5 \hat{j}}{0.7}$ $\vec{v}_{cm} = \frac{3.5}{0.7} \hat{i} + \frac{2.5}{0.7} \hat{j}$ $\vec{v}_{cm} = 5 \hat{i} + \frac{25}{7} \hat{j} \ m/s$.

Two objects of masses $200 \ gm$ and $500 \ gm$ possess velocities $10 \hat{i} \ m/s$ and $3 \hat{i} + 5 \hat{j} \ m/s$ respectively. The velocity of their centre of mass in $m/s$ is

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