Question

Centre of mass of two particles with masses 2 kg and 1 kg located at (1, 0, 1) and (2, 2, 0) has the co-ordinates of

• A. $\frac{4}{3},\frac{2}{3},\frac{2}{3}$
• B. $\frac{2}{3},\frac{4}{3},\frac{2}{3}$
• C. $\frac{2}{3},\frac{2}{3},\frac{4}{3}$
• D. $\frac{1}{3},\frac{2}{3},\frac{2}{3}$

Answer 1

The correct option is A $\frac{4}{3},\frac{2}{3},\frac{2}{3}$

Center of mass is $\frac{m_1\times r_1+m_2\times r_2}{m_1+m_2}$

hence putting values the given questions center of the mass of the system

$x$ coordinate$:$ $\frac{2\times 1+1\times 2}{2+1}=\frac{4}{3}$

$y$ coordinate$:$ $\frac{2\times 0+1\times 2}{2+1}=\frac{2}{3}$

$z$ coordinate$:$ $\frac{2\times 1+1\times 0}{2+1}=\frac{2}{3}$

$x,y,z=$ $\frac{4}{3}+\frac{2}{3}+\frac{2}{3}$

Hence,

option $\left(A\right)$ is correct answer.