Centre of mass of 3 particles 10 kg, 20 kg and 30 kg is at (0, 0, 0). Where should a particle of mass 40 kg be placed so that the combination centre of mass will be at (3,3,3)

Options

A. (0,0,0)
B. (7.5,7.5,7.5)
C. (1,2,3)
D. (4,4,4)

Answer

B

Explanation

`m_(1)=10+20+30=60kg" "m_(2)=40`
`(x_(1),y_(1),z_(1))=(0,0,0)(x_(2),y_(2),y_(2))`
`x_(cm),y_(cm),2_(cm)=(3,3,3)`
`x_(cm)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))`
`3=(60(0)+40x_(2))/(60+40)`
Similarly calculate for `y_(2)` and `z_(2)`