A) \[\left( \frac{2+2\sqrt{3}}{3} \right)\,\hat{i}-\frac{2}{3}\hat{j}\]
B) \[4\,\hat{i}\]
C) \[\left( \frac{2-2\sqrt{3}}{3} \right)\,\hat{i}-\frac{1}{3}\hat{j}\]
D) None of these
Correct Answer: A
Solution :
\[{{\operatorname{m}}_{1}}\,\,=\,\,1 kg, \,{{v}_{1}}=2\,\hat{i}\] \[{{\operatorname{m}}_{2}}\,\,=\,\,2kg,\,\,{{v}_{2}}=2\,cos\,30{}^\circ \,\,\hat{i}-2sin30{}^\circ \,\hat{j}\] \[{{v}_{cm}}=\frac{{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\,\,\,\frac{1\times 2\,\hat{i}+2(2\,cos\,\,30{}^\circ \,\hat{i}-2\,\sin \,30{}^\circ \hat{j})}{1+2}\] \[=\,\,\,\frac{2\hat{i}+2\sqrt{3}\,\hat{i}-2\hat{j}}{3}\,\,=\,\,\left( \frac{2+2\sqrt{3}}{3} \right)\hat{i}-\frac{2}{3}\hat{j}\]
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