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

Options

A. `r_(1) + r_(2)`
B. `2(r_(1) + r_(2))`
C. `r_(1) - r_(2)`
D. `(r_(1) + r_(2))/(2)`

Answer

D

Explanation

Given, position vector of the first particle `= r_(1)`
Position vector of second particle `= r_(2)`
We know that,
Centre of mass of system
`= (m_(1)r_(1) xx m_(2)r_(2))/(m_(1) + m_(2))`
`= (m r_(1) + m r_(2))/(m + m)`
`= (m(r_(1) + r_(2)))/(2m) = (r_(1) + r_(2))/(2)`