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Four particles of mass 1 kg, 2kg, 3kg an...

Four particles of mass 1 kg, 2kg, 3kg and 4kg are placed at the four verticles, A, B,C and D of a square of side 1m. Find the position of center of mass of the particles.

Text Solution

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Assuming A as the origin, AB as x-axis and AD as y-axis we have

Co-ordinates of their CM are
`X_(CM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3)+m_(4)x_(4))/(m_(1)+m_(2)+m_(3)+m_(4))`
`= ((1)(0)+2(1)+3(1)+4(0))/(1+2+3+4)=0.5 m`
Similarly, `y_(CM)=`
`(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3)+m_(4)y_(4))/(m_(1)+m_(2)+m_(3)+m_(4))=(1(0)+2(0)+3(1)+4(1))/(1+2+3+4)=0.7 m`
`therefore` Co-ordinates of centre of mass `(X_(CM), y_(CM))=(0.5 m, 0.7 m)`
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