A) \[r,r/2\]
B) \[r,r/3\]
C) \[\frac{\sqrt{{}}3}{2}r,r\]
D) \[r,r\sqrt{{}}3\]
Correct Answer: D
Solution :
: Let A be origin (0, 0) Coordinates of\[B=(2r,\text{ }0)\] Coordinates of \[C=(r,\sqrt{3}r)\] \[\overline{x}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}+{{m}_{3}}{{x}_{3}}}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\] \[=\frac{0+(m\times 2r)+(m\times r)}{m+m+m}=\frac{3mr}{3m}=r\] \[\overline{y}=\frac{{{m}_{1}}{{y}_{1}}+{{m}_{2}}{{y}_{2}}+{{m}_{3}}{{y}_{3}}}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}=\frac{0+0+m\times \sqrt{3}r}{m+m+m}\] \[=\frac{\sqrt{3}mr}{3m}=\frac{r}{\sqrt{3}}\] \[\therefore \]Centre of mass\[=(r,r/\sqrt{3})\].You need to login to perform this action.
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