A) \[\sqrt{3}(\hat{i}-\hat{j})\]
B) \[\frac{{\hat{i}}}{\sqrt{3}}+\hat{j}\]
C) \[\frac{\hat{i}+\hat{j}}{3}\]
D) \[\hat{i}+\frac{{\hat{j}}}{\sqrt{3}}\]
Correct Answer: D
Solution :
The\[x\]co-ordinate of centre of mass is \[\overline{x}=\frac{\Sigma {{m}_{i}}{{x}_{i}}}{\Sigma {{m}_{i}}}\] \[=\frac{m\times 0+m\times 1+m\times 2}{m+m+m}=1\] \[\overline{y}=\frac{\Sigma {{m}_{i}}{{y}_{i}}}{\Sigma {{m}_{i}}}\] \[=\frac{m\times 0+m(2\sin {{60}^{o}})+m\times 0}{m+m+m}\] \[\overline{y}=\frac{\sqrt{3}m}{3m}=\frac{1}{\sqrt{3}}\] Position vector of centre of mass is\[\left( \hat{i}+\frac{{\hat{j}}}{\sqrt{3}} \right).\]You need to login to perform this action.
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