Question

Two bodies of mass $1\text{Kg}$ and $3\text{Kg}$ 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. $-2\hat{i}+2\hat{k}$

Answer 1

The correct option is A $-2\hat{i}-\hat{j}+\hat{k}$

We know that,

${\overrightarrow{r}}_{com}=\frac{m_1{\overrightarrow{r}}_1+m_2{\overrightarrow{r}}_2}{m_1+m_2}$

${\overrightarrow{r}}_1=\hat{i}+2\hat{j}+\hat{k}$

${\overrightarrow{r}}_2=-3\hat{i}-2\hat{j}+\hat{k}$

${\overrightarrow{r}}_{com}=\frac{1(\hat{i}+2\hat{j}+\hat{k})+3(-3\hat{i}-2\hat{j}+\hat{k})}{1+3}$

${\overrightarrow{r}}_{com}=\frac{-8\hat{i}-4\hat{j}+4\hat{k}}{4}$

${\overrightarrow{r}}_{com}=-2\hat{i}-\hat{j}+\hat{k}$

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