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

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Aicharya · Accepted Answer

Given, $m_1=6 \mathrm{~kg}, m_2=4 \mathrm{~kg}$ $\overrightarrow{\mathbf{v}}_1=5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+10 \hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{v}}_2=10 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ The velocity of centre of mass is $\begin{aligned} \overrightarrow{\mathbf{v}} & =\frac{m_1 \overrightarrow{\mathbf{v}}_1+m_2 \overrightarrow{\mathbf{v}}_2}{m_1+m_2} \ & =\frac{6(5 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+10 \hat{\mathbf{k}})+4(10 \hat{\mathbf{i}}-2 \hat{\mathbf{i}}+5 \hat{\mathbf{k}})}{6+4} \ & =\frac{70 \hat{\mathbf{i}}-20 \hat{\mathbf{j}}+80 \hat{\mathbf{k}}}{10} \ & =7 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+8 \hat{\mathbf{k}}\end{aligned}$

Two bodies of $6 \mathrm{~kg}$ and $4 \mathrm{~kg}$ masses have their velocity $5 \hat{\mathbf{i}}-2…

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