Question

Two particles whose masses are $10kg$ and $30kg$ and their position vectors are $\hat{i}+\hat{j}+\hat{k}$ and $-\hat{i}-\hat{j}-\hat{k}$ respectively would have the centre of mass at

• A. $-\frac{\left(\hat{i}+\hat{j}+\hat{k}\right)}{2}$
• B. $\frac{\left(\hat{i}+\hat{j}+\hat{k}\right)}{2}$
• C. $-\frac{\left(\hat{i}+\hat{j}+\hat{k}\right)}{4}$
• D. $\frac{\left(\hat{i}+\hat{j}+\hat{k}\right)}{4}$

Answer 1

Answer: (A)

$\overrightarrow{r_{cm}}=\frac{m_1\overrightarrow{r_1}+m_2\overrightarrow{r_2}}{m_1{m}_2}$
$\Rightarrow \overrightarrow{r_{cm}}=\frac{10\left(\hat{i}+\hat{j}+\hat{k}\right)+30\left(-\hat{i}-\hat{j}-\hat{k}\right)}{40}$
$\Rightarrow \overrightarrow{r_{cm}}=\frac{-20\left(\hat{i}+\hat{j}+\hat{k}\right)}{40}$
$\Rightarrow \overrightarrow{r_{cm}}=-\frac{\left(\hat{i}+\hat{j}+\hat{k}\right)}{2}$