A) \[\frac{1}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j}\]
B) \[\frac{1}{2}\hat{i}+\frac{1}{2\sqrt{3}}\hat{j}\]
C) \[\hat{i}+\hat{j}\]
D) \[2\hat{i}-\hat{j}\]
Correct Answer: B
Solution :
\[{{X}_{CM}}=\frac{\Sigma {{m}_{i}}{{x}_{i}}}{\Sigma {{m}_{i}}}=\frac{m\times 0+m\times 1+m+\frac{1}{2}}{m+m+m}\] \[=\frac{3m/2}{3m}=\frac{1}{2}\] \[{{Y}_{cm}}=\frac{\Sigma {{m}_{i}}{{y}_{i}}}{\Sigma {{m}_{i}}}=\frac{m\times 0+m\times 1\times \sin 60+m\times 0}{3m}\] \[=\frac{\sqrt{3}m/2}{3m}=\frac{1}{2\sqrt{3}}\] So, position vector of centre of mass is\[\left( \frac{1}{2}\hat{i}+\frac{1}{2\sqrt{3}}\hat{j} \right)\]You need to login to perform this action.
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