A) \[\left( \frac{8}{9},\frac{13}{9} \right)\]
B) \[\left( \frac{7}{9},\frac{11}{9} \right)\]
C) \[\left( \frac{11}{9},\frac{13}{9} \right)\]
D) \[\left( \frac{11}{9},\frac{8}{9} \right)\]
Correct Answer: A
Solution :
Co-ordinates of the corners of the square are \[(0,0),\] \[(2,0),\] \[(2,2),\]\[(0,2)\]. \[\therefore \] \[{{x}_{CM}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}+{{m}_{3}}{{x}_{3}}+{{m}_{4}}{{x}_{4}}}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}+{{m}_{4}}}\] \[=\frac{2\times 0+3\times 2+5\times 2+8\times 0}{2+3+5+8}=\frac{8}{9}\,\,m\] \[{{y}_{CM}}=\frac{{{m}_{1}}{{y}_{1}}+{{m}_{2}}{{y}_{2}}+{{m}_{3}}{{y}_{3}}+{{m}_{4}}{{y}_{4}}}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}+{{m}_{4}}}\] \[=\frac{2\times 0+3\times 0+5\times 2+8\times 2}{2+3+5+8}=\frac{13}{9}\,m\] Hence co-ordinates of the centre of mass are \[\left( \frac{8}{9},\frac{13}{9} \right)\]
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