Question

Two masses of $6$ and $2$ unit are at positions $\left(6\hat{i}-7\hat{j}\right)$ and $\left(2\hat{i}+5\hat{j}-8\hat{k}\right)$ , respectively. The coordinates of the centre of mass $(CM)$ are

• A. $(2,-5,3)$
• B. $(5,-5,-3)$
• C. $(5,-4,-2)$
• D. $(5,-4,-4)$

Answer 1

Answer: (C)

Given, masses $m_1=6$ unit
$m_2=2$ unit
positions $6\hat{i}-7\hat{j}$ and $2\hat{i}+5\hat{j}-8\hat{k}$
To find centre of mass
$x_{cor}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$
$=\frac{6\times 6+2\times 2}{6+2}=\frac{36+4}{8}=5\hat{i}$
$Y_{cor}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$
$=\frac{6\times \left(-7\right)+2\times \left(+5\right)}{6+2}=\frac{-42+10}{8}=-4\hat{j}$
$Z_{cor}=\frac{m_1{z}_1+m_2{z}_2}{m_1+m_2}$
$=\frac{6\times \left(0\right)+2\times \left(-8\right)}{2+6}=\frac{-16}{8}=-2\hat{k}$
$\therefore$ Centre of mass lies on $5\hat{i}-4\hat{j}-2\hat{k}$