A) \[\frac{3}{5}\mathbf{\hat{i}}+\frac{4}{5}\mathbf{\hat{j}}\]
B) \[(3\mathbf{\hat{i}}+\mathbf{\hat{j}})\]
C) \[\frac{2}{5}\mathbf{\hat{i}}+\frac{4}{5}\mathbf{\hat{j}}\]
D) \[\frac{1}{5}\mathbf{\hat{i}}+\frac{3}{5}\mathbf{\hat{j}}\]
Correct Answer: A
Solution :
\[{{\vec{v}}_{CM}}=\frac{{{m}_{1}}{{{\vec{v}}}_{1}}+{{m}_{2}}{{{\vec{v}}}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{2\times (1\hat{i})+4(1\hat{i}+1\hat{j})+4(1\hat{j})}{2+4+4}=\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j}\]
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