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 :
\[{{\overrightarrow{\mathbf{v}}}_{cm}}=\frac{{{m}_{1}}\,{{\overrightarrow{\mathbf{v}}}_{1}}+{{m}_{2}}\,{{\overrightarrow{\mathbf{v}}}_{2}}\,}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{2\times (1\,\,\mathbf{\hat{i}})+4(1\,\,\mathbf{\hat{i}}+i\,\,\mathbf{\hat{j}})+4(1\,\mathbf{\hat{j}})}{2+4+4}=\frac{3}{5}\mathbf{\hat{i}}+\frac{4}{5}\mathbf{\hat{j}}\]
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