Q. Four particles, each of mass 1 kg, are placed at the corners of a square of side 1m in the X- Y plane. If the point of intersection of the diagonals of the square, is taken as the origin, the co-ordinates of the centre of mass are:
EAMCETEAMCET 2004System of Particles and Rotational Motion
Solution:
Given: $ {{m}_{1}}={{m}_{2}}={{m}_{3}}={{m}_{4}}=1\,kg $ $ AB=BC=CD=DA=1m $
Hence, the co-ordinates of A, B, C, D are given in the figure, from the relation for $ {{x}_{cm}} $ is $ {{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{1\times 0.5+1\times 0.5+1(-0.5)+1\times (-0.5)}{1+1+1+1}=0 $ $ {{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{1\times 0.5+1\times (-0.5)+1\times (-0.5)+1\times (0.5)}{1+1+1+1} $ Co-ordinates of centre of mass will be (0,0).
