question_answer

Three bodies having equal masses m are placed at (a, 0), (0, 0) and,\[\left( \frac{a}{2},\,\,\frac{a\sqrt{3}}{2} \right)\]. The coordinates of centre of mass \[{{x}_{CM}}\] and \[{{y}_{CM}}\] are respectively

A)  \[\frac{a\sqrt{3}}{6},\,\,\frac{a}{2}\]                

B)  \[\frac{a}{2},\,\,\frac{a\sqrt{3}}{6}\]

C)  \[\frac{a\sqrt{3}}{2},\,\,\frac{a}{6}\]                

D)  \[\frac{a}{6},\,\,\frac{a\sqrt{3}}{2}\]

Correct Answer: B

Solution :

\[{{X}_{CM}}=\frac{0\times m+a\times m+\frac{a}{2}\times m}{m+m+m}=\frac{a}{2}\] And \[{{y}_{CM}}=\frac{0\times m+a\times m+\frac{a\sqrt{3}}{2}\times m}{m+m+m}=\frac{a\sqrt{3}}{6}\]