Q. A system consists of 3 particles each of mass $m$ located at point (1, 1), (2, 2) and (3, 3). The coordinates of the center of mass are

A) (6, 6)
B) (3, 3)
C) (1, 1)
D) (2, 2)
Explanation

(d) If $n$ masses are equal
$m_{1} = m_{2} = m_{3} = .... = m_{n}$
Then position vector of centre of mass.
The coordinate of the centre of mass
$(x,y) = \left( \frac{m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3}}{m_{1} + m_{2} + m_{3}},\ \frac{m_{1}y_{1} + m_{2}y_{2} + m_{3}y_{3}}{m_{1} + m_{2} + m_{3}} \right)$
$= \left( \frac{m + 2m + 3m}{3m},\frac{m + 2m + 3m}{3m} \right)$
$= \left( \frac{6m}{3m},\frac{6m}{3m} \right)$
$= (2,2)$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.