Question

The coordinates of the positions of particles of mass 7,4 and 10 gm (1,5,-3), (2,5,7) and (3,3,-1) cm respectively. The position of the centre of mass of the system would be

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$m_1=7gm,m_2=4gm,m_3=10gm$ and $\overrightarrow{r_1}=(\hat{i}+5\hat{j}-3\hat{k}),r_2=(2i+5j+7k),r_3=(3\hat{i}+3\hat{j}-\hat{k})$
Position vector of centre mass $\overrightarrow{r}=\frac{7(\hat{i}+5\hat{j}-3\hat{k})+4(2\hat{i}+5\hat{j}+7\hat{k})+10(3\hat{i}+3\hat{j}-\hat{k})}{7+4+10}$
$=\frac{(45\hat{i}+85\hat{j}-3\hat{k})}{21}$
$\Rightarrow \overrightarrow{r}=\frac{15}{7}\hat{i}+\frac{85}{21}j-\frac{1}{7}\hat{k}.$ So coordinates of centre of mass $\left[\begin{array}{ccc}\frac{15}{7},& \frac{85}{21},& \frac{-1}{7}\end{array}\right].$