A) \[-\frac{3}{4}(\hat{i}-\hat{j}-\hat{k})\]
B) \[-\frac{1}{4}(\hat{i}-\hat{j}-\hat{k})\]
C) \[-\frac{1}{2}(\hat{i}-\hat{j}-\hat{k})\]
D) \[-(\hat{i}-\hat{j}-\hat{k})\]
Correct Answer: C
Solution :
Here, \[{{m}_{1}}=1\,kg,\] \[{{\vec{r}}_{1}}=\hat{i}+\hat{j}+\hat{k}\] \[{{m}_{2}}=3\,kg,\] \[{{\vec{r}}_{2}}=-\hat{i}-\hat{j}+\hat{k}\] From the relation for position vector of centre of mass \[{{\vec{r}}_{cm}}=\frac{{{m}_{1}}{{{\vec{r}}}_{1}}+{{m}_{2}}{{{\vec{r}}}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{1(\hat{i}+\hat{j}+\hat{k})+3(-\hat{i}-\hat{j}-\hat{k})}{4}\] \[=\frac{-2\hat{i}-2\hat{j}-2\hat{k}}{4}\] \[=-\frac{1}{2}(\hat{i}+\hat{j}+\hat{k})\]
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