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The co ordinates of centre of mass of mass of paricle of mass 10,20,30gm are (1,1,1)cm.The position co ordinates of mass 40 gm which when added to the system,the position of combined centre of mass be at(0,0,0) are,

Asked by gantasasidharreddy 20th August 2018, 9:50 PM
Answered by Expert
Answer:
Let Initially the system has three masses 10 gm, 20 gm and 30 gm with x repective x-xoordinates x1, x2 and x3.
 
Then x-coordinate of centre of mass is given by :- begin mathsize 12px style fraction numerator 10 x subscript 1 plus 20 x subscript 2 plus 30 x subscript 3 over denominator 10 plus 20 plus 30 end fraction space equals space 1 space left parenthesis g i v e n right parenthesis space comma space o r space space 10 x subscript 1 plus 20 x subscript 2 plus 30 x subscript 3 space space equals space 60 space................. left parenthesis 1 right parenthesis
end style
After adding 4th mass 40 gm that has x-coordinate x4, x-coordinate of centre of mass of new system is given by
 
begin mathsize 12px style space space 10 x subscript 1 plus 20 x subscript 2 plus 30 x subscript 3 plus 40 x subscript 4 space space equals space 0 space................. left parenthesis 2 right parenthesis
end style
by solving eqn.(1) and (2), we get x4 = -1.5.
 
Similar calculations can be performed to get y and z coordinates, we get coordinates of comibined system as (-1.5, -1.5, -1.5)
Answered by Expert 21st August 2018, 9:47 AM
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