A) \[\hat{i}+3\hat{j} -2\hat{k}\]
B) \[-\hat{i}-3\hat{j} -2\hat{k}\]
C) \[-\hat{i}+3\hat{j} +2\hat{k}\]
D) \[-\hat{i}+3\hat{j} -2\hat{k}\]
Correct Answer: D
Solution :
Position vector of centre of mass \[{{\operatorname{r}}_{cm}}=\frac{{{m}_{1}}{{r}_{1}}+{{m}_{2}}{{r}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[{{r}_{1}}=2\hat{i}+3\hat{j}+4\hat{k}, m =1kg\] \[{{r}_{2}}=-2\hat{i}+3\hat{j}-4\hat{k}, {{m}_{2}} =3kg\] \[{{r}_{\operatorname{cm}}}=\frac{1\left( 2\hat{i}+3\hat{j}-4\hat{k} \right)+3\left( -2\hat{i}+3\hat{j}-4\hat{k} \right)}{1+3}\] \[=\frac{-4\hat{i}+12\hat{j}-8\hat{k}}{4}\] \[=-\hat{i}+3\hat{j}-2\hat{k}\]
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