Question

If two identical particles are at (2,3,4) and (6,3,2) then co-ordinates of centre of mass of the system are​

Answer 1

Given:

Two identical particles are at (2,3,4) and (6,3,2).

To find:

Coordinates of Centre of Mass ?

Calculation:

The coordinates of the Centre of Mass is:

$\sf = \bigg ( \dfrac{mx_{1} + mx_{2} }{m + m} ,\dfrac{my_{1} + my_{2} }{m + m},\dfrac{mz_{1} + mz_{2} }{m + m} \bigg)$

$\sf = \bigg ( \dfrac{mx_{1} + mx_{2} }{2m} ,\dfrac{my_{1} + my_{2} }{2m},\dfrac{mz_{1} + mz_{2} }{2m} \bigg)$

$\sf = \bigg ( \dfrac{x_{1} + x_{2} }{2} ,\dfrac{y_{1} + y_{2} }{2},\dfrac{z_{1} + z_{2} }{2} \bigg)$

$\sf = \bigg ( \dfrac{2 + 6 }{2} ,\dfrac{3 + 3 }{2},\dfrac{4 + 2}{2} \bigg)$

$\sf = \bigg ( \dfrac{8}{2} ,\dfrac{6 }{2},\dfrac{6}{2} \bigg)$

$\sf = \bigg ( 4,3,3 \bigg)$

So, required coordinates is (4,3,3).