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(C) Given,$m_1 = 6 \ kg, m_2 = 4 \ kg$. $\overrightarrow{v}_1 = 5 \hat{i} - 2 \hat{j} + 10 \hat{k}, \quad \overrightarrow{v}_2 = 10 \hat{i} - 2 \hat{j

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$7 \hat{i}-2 \hat{j}+8 \hat{k}$

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(C) Given,$m_1 = 6 \ kg, m_2 = 4 \ kg$. $\overrightarrow{v}_1 = 5 \hat{i} - 2 \hat{j} + 10 \hat{k}, \quad \overrightarrow{v}_2 = 10 \hat{i} - 2 \hat{j} + 5 \hat{k}$. The velocity of the centre of mass is given by the formula: $\overrightarrow{v}_{cm} = \frac{m_1 \overrightarrow{v}_1 + m_2 \overrightarrow{v}_2}{m_1 + m_2}$. Substituting the values: $\overrightarrow{v}_{cm} = \frac{6(5 \hat{i} - 2 \hat{j} + 10 \hat{k}) + 4(10 \hat{i} - 2 \hat{j} + 5 \hat{k})}{6 + 4}$. $\overrightarrow{v}_{cm} = \frac{(30 \hat{i} - 12 \hat{j} + 60 \hat{k}) + (40 \hat{i} - 8 \hat{j} + 20 \hat{k})}{10}$. $\overrightarrow{v}_{cm} = \frac{70 \hat{i} - 20 \hat{j} + 80 \hat{k}}{10}$. $\overrightarrow{v}_{cm} = 7 \hat{i} - 2 \hat{j} + 8 \hat{k}$.

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

Similar Questions

Which of the following is the correct order of stability for alkali metal chlorides?

Match the following:
| Column $I$ | Column $II$ |
| :--- | :--- |
| $A$. Hooke's law | $1$. Tangential strain |
| $B$. Shearing strain | $2$. Temporary loss of elastic property |
| $C$. Bulk strain | $3$. Elastic limit |
| $D$. Elastic fatigue | $4$. $3$ times the linear strain |

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