A) \[\left( \frac{4}{3},1 \right)\]
B) \[\left( \frac{1}{3},\frac{2}{3} \right)\]
C) \[\left( \frac{1}{2},\frac{1}{2} \right)\]
D) \[\left( 1,\,\frac{4}{3} \right)\]
Correct Answer: D
Solution :
[d] \[{{X}_{CM}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}+{{m}_{3}}{{x}_{3}}}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\] \[=\frac{1\times 0+1\times 3+1\times 0}{1+1+1}\] \[{{Y}_{CM}}=\frac{{{m}_{1}}{{y}_{1}}+{{m}_{2}}{{y}_{2}}+{{m}_{3}}{{y}_{3}}}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\] \[=\frac{1\times 0+1\times 0+1\times 4}{1+1+1}=\frac{4}{3}\] Therefore the coordinates of centre of mass are \[\left( 1,\frac{4}{3} \right)\]
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