1.

The coordinates of a triangle `ABC` are `A(1,2)`, `B(4,6)` and `C(-3,-2)`. Three particles of masses `1kg`, `2kg` and `m kg` are placed the vertices of the triangle. If the coordinate of the centre of mass are `((3)/(5),2)`, calculate the mass `m`.

Answer» `x_(cm)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))=(3)/(5)`
`implies(1+8-3m)/(3+m)=(3)/(5)`
`implies(9-3m)/(3+m)=(3)/(5)`
`implies45-15m=9+3m`
`implies36=18m`
`impliesm=2 kg`
Or
Alternate method
`y_(cm)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3))=2`
`implies(2+12-2m)/(3+m)=2`
`implies14-2m=6+2m`
`implies8=4m`
`m=2kg`


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