Question

The coordinates of the centre of mass of a system of three particles of masses $1 \, mg$ , $2 \, mg$ and $3 \, mg$ are $\left(2 , \, 2 , \, 2\right)$ . The coordinates of the fourth particle of mass $4 \, mg$ to be positioned so that the centre of mass of the four particles system is at the origin of the three-dimensional rectangular coordinate system are

• A. $\left(1 , \, 1 , \, 1\right)$
• B. $\left(2 , \, 2 , \, 2\right)$
• C. $\left(3 , \, 3 , \, 3\right)$
• D. $\left(- 3 , \, - 3 , \, - 3\right)$

Answer 1

Answer: (D)

Treat the three masses of $1 \, mg, \, 2 \, mg$ and $3 \, mg$ as a single mass of $6 \, mg \, at \, \left(2 , \, 2 , \, 2\right)$
Now, $0=\frac{4 \times x + 6 \times 2}{10} \, or \, 4x+12=0$
Or $x=-3,$
and, $0=\frac{4 \times y + 6 \times 2}{10} \, or \, y=-3$
Similarly, $z=-3$