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If the centre of mass of three particles of masses of 1kg, 2kg, 3kg is at (2,2,2), then where should a fourth particle of mass 4kg be placed so that the combined centre of mass may be at (0,0,0).

Answer» <html><body><p></p>Solution :Let `(x_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>),y_(1),z_(1)),(x_(2),y_(2),z_(2))` and `(x_(3),y_(3),z_(3))` be the positions of masses `1kg`, `2kg`, `3kg` and let the co-ordinates of centre of mass of the three particle system is `(x_(cm),y_(cm),z_(cm))` respectively. <br/> `x_(cm)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))` <br/> `implies2=(1xx x_(1)+2xx x_(2)+<a href="https://interviewquestions.tuteehub.com/tag/3xx-1865440" style="font-weight:bold;" target="_blank" title="Click to know more about 3XX">3XX</a> x_(3))/(1+2+3)` <br/> (or) `x_(1)+2x_(2)+3x_(3)=12`.............`(1)` <br/> Suppose the <a href="https://interviewquestions.tuteehub.com/tag/fourth-998521" style="font-weight:bold;" target="_blank" title="Click to know more about FOURTH">FOURTH</a> particle of mass `4kg` is placed at `(x_(1),y_(1),z_(1))` so that centre of mass of <a href="https://interviewquestions.tuteehub.com/tag/new-1114486" style="font-weight:bold;" target="_blank" title="Click to know more about NEW">NEW</a> system <a href="https://interviewquestions.tuteehub.com/tag/shifts-1205400" style="font-weight:bold;" target="_blank" title="Click to know more about SHIFTS">SHIFTS</a> to `(0,0,0)`. For X-co-ordinate of new centre of mass we have <br/> `0=(1xx x_(1)+2xx x_(2)+3xx x_(3)+4xx x_(4))/(1+2+3+4)` <br/> `impliesx_(1)+2x_(2)+3x_(3)+4x_(4)=0`...........`(2)` <br/> From equations `(1)` and `(2)` <br/> `12+4x_(4)=0impliesx_(4)=-3` <br/> Similarly `y_(4)=-3` and `x_(4)=-3` <br/> Therefore 4kg should be placed at `(-3,-3,-3)`.</body></html>


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