Question

The position vectors of two identical particles with respect to the origin in the three-dimensional coordinate system are $r_{1}$ and $r_{2}$ . The position vector of the centre of mass of the system is given by

• A. $r_{1}+r_{2}$
• B. $2\left(r_{1} + r_{2}\right)$
• C. $r_{1}-r_{2}$
• D. $\frac{r_{1} \, + \, r_{2}}{2}$

Answer 1

Answer: (D)

Given, position vector of first particle $=r_{1}$
Position vector of second particle $=r_{2}$
$m_{1}=m_{2}=m$
We know that,
Centre of mass of system
$=\frac{m_{1} r_{1} + m_{2} r_{2}}{m_{1} + m_{2}}$
$=\frac{m r_{1} + m r_{2}}{m + m}$
$=\frac{m \left(r_{1} + r_{2}\right)}{2 m}=\frac{r_{1} + r_{2}}{2}$