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Centre of mass of three particles of mas...

Centre of mass of three particles of masses `1 kg, 2 kg and 3 kg` lies at the point `(1,2,3)` and centre of mass of another system of particles `3 kg and 2 kg` lies at the point `(-1, 3, -2)`. Where should we put a particle of mass `5 kg` so that the centre of mass of entire system lies at the centre of mass of first system ?

A

(0, 0, 0)

B

(1, 3, 2)

C

(-1, 2, 3)

D

(3, 1, 8)

Text Solution

Verified by Experts

The correct Answer is:
D
According to the definition of center of mass, we can imagine one particle of mass `(1+2+3)` kg at (1,2,3), another particle of mass (2+3) kg at `(-1,3,-2)`. Let the third particle of mass 5 kg put at `(x_(3),y_(3),z_(3))` i.e.,
`m_(1)=6kg, (x_(1),y_(1),z_(1))=(1,2,3)`
`m_(2)=5kg, (x_(2),y_(2),z_(2))=(-1,3,-2)`
`m_(3)=5kg, (x_(3),y_(3),z_(3))=?`
Given, `(X_(CM), Y_(CM), Z_(CM))= 1,2,3`
Using `X_(CM) = (m_(1)x_(2)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`1= (6 xx 1+5 xx (-1)+5x_(3))/(6+5+5)`
`5x_(3)=16-1=15` or `x_(3)=3`
Similarly, `y_(3)=1` and `z_(3)=8`
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