Question

Three particles of the same mass lie in the x–y plane. The (x, y) coordinates of their positions are (1, 1), (2, 2) and (3, 3) respectively. The (x, y) coordinates of the centre of mass are

• A. (1, 2)
• B. (2, 2)
• C. (4, 2)
• D. (6, 6)

Answer 1

The correct option is B (2, 2)

The x and y co-ordinates of the centre of mass are
$x=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3}{m_1+m_2+m_3}=\frac{1}{3}(x_1+x_2+x_3)(\because m_1=m_2=m_3)$
$=\frac{1}{3}(1+2+3)=2$
and $=\frac{1}{3}(y_1+y_2+y_3)=\frac{1}{3}(1+2+3)=2$
Hence the correct choice is (b).