Question

Particles of mass 2 gm, 3 gm, 5 gm and 6 gm are placed at the points (-6, 1), (5, 0), (-3, 2) and (2, -2) respectively. The co-ordinates of the centre of mass of the system will be

• A. (-1, 1)
• B. (-1/4, 1/4)
• C. (1, -1)
• D. (0, 0)

Answer 1

The correct option is D

(0, 0)

$x_{cm}=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3+m_4{x}_4}{m_1+m_2+m_3+m_4}=\frac{2(-6)+3\left(5\right)+5(-3)+6\left(2\right)}{2+3+5+6}=0$

$y_{cm}=\frac{m_1{y}_1+m_2{y}_2+m_3{y}_3+m_4{y}_4}{m_1+m_2+m_3+m_4}=\frac{2\left(1\right)+3\left(0\right)+5\left(2\right)+6(-2)}{2+3+5+6}=0$

$\therefore (x_{cm},y_{cm})=(0,0)$