The position vectors of two identical particles with respect to the origin in the three-dimensional coordinate system are r1 and r2 . The position vector of the centre of mass of the system is given by

Question

The position vectors of two identical particles with respect to the origin in the three-dimensional coordinate system are r1 and r2 . The position vector of the centre of mass of the system is given by (A) r1+r2 (B) 2(r1 + r2) (C) r1-r2 (D) (r1 + r2/2)

Tardigrade Admin · Accepted Answer

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 ( r _{1} + r _{2} )}{2 m} = \frac{r _{1} + r _{2}}{2}

Q. 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

$r_{1} + r_{2}$

$2 (r_{1} + r_{2})$

$r_{1} - r_{2}$

$\frac{r _{1} + r _{2}}{2}$

Q. The position vectors of two identical particles with respect to the origin in the three-dimensional coordinate system are r1​ and r2​ . The position vector of the centre of mass of the system is given by

r1​+r2​

2(r1​+r2​)

r1​−r2​

2r1​+r2​​

Given, position vector of first particle =r1​ Position vector of second particle =r2​ m1​=m2​=m We know that, Centre of mass of system =m1​+m2​m1​r1​+m2​r2​​ =m+mmr1​+mr2​​ =2mm(r1​+r2​)​=2r1​+r2​​

Q. 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

$r_{1} + r_{2}$

$2 (r_{1} + r_{2})$

$r_{1} - r_{2}$

$\frac{r _{1} + r _{2}}{2}$