Question

Two bodies of mass $1\, kg$ and $3\, kg$ have position vectors $\hat{ i }+2 \hat{ j }+\hat{ k }$ and $-3 \hat{ i }-2 \hat{ j }+\hat{ k }$, respectively. The centre of mass of this system has a position vector:

• A. $-2\hat{i}-\hat{j}+\hat{k}$
• B. $2\hat{i}-\hat{j}-2\hat{k}$
• C. $-\hat{i}+\hat{j}+\hat{k}$
• D. $-2\hat{i}+\hat{k}$

Answer 1

Answer: (A)

The position vector of centre of mass
$\vec{r}=\vec{r}=\frac{m_{1} \vec{r}_{1}+m_{2} \vec{r}_{2}}{m_{1}+m_{2}} $
ltbrtgt $=\frac{1(\hat{i}+2 \hat{j}+\hat{k})+3(-3 \hat{i}-2 \hat{j}+\hat{k})}{1+3} $
$=\frac{1}{4}(-8 \hat{i}-4 \hat{j}+4 \hat{k})$
$=-2 \hat{i}-\hat{j}+\hat{k} $