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
$x_{cor}=\frac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}$
$=\frac{6\times6+2\times2}{6+2}=\frac{36+4}{8}=5\hat{i}$
$Y_{cor} =\frac{m_{1}y_{1}+m_{2}y_{2}}{m_{1}+m_{2}}$
$=\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 $5\hat{i}-4\hat{j}-2\hat{k}$