Q. Two bodies of mass $1\ kg$ and $3\ kg$ have position vectors $\widehat{i} + 2\widehat{j} + \widehat{k}$ and $- 3\widehat{i} - 2\widehat{j} + \widehat{k}$, respectively. The centre of mass of this system has a position vector
A) $- 2\widehat{i} + 2\widehat{k}$
B) $- 2\widehat{i} - \widehat{j} + \widehat{k}$
C) $2\widehat{i} - \widehat{j} - \widehat{k}$
D) $- \widehat{i} + \widehat{j} + \widehat{k}$
Explanation
(b) ${\overrightarrow{r}}_{cm} = \frac{m_{1}\overrightarrow{r_{1}} + m_{2}\overrightarrow{r_{2}}}{m_{1} + m_{2}} = \frac{1\left( \widehat{i} + 2\widehat{j} + \widehat{k} \right) + 3( - 3\widehat{i} - 2\widehat{j} + \widehat{k})}{1 + 3}$
$\Rightarrow {\overrightarrow{r}}_{cm} = - 2\widehat{i} - \widehat{j} + \widehat{k}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.