Question

two bodies of masses 0.5kg and 1kg are lying in the x-y plane at points (-1,2) and (3,4) respectively .Locate the centre of mass of the system

Answer 1

The center of mass of a system of two particles of masses m1 and m2 each separated by a distance x1 and x2 from the considered axis of rotation respectively, is,

$x=\dfrac {m_1x_1+m_2x_2}{m_1+m_2}$

Thus, for a double coordinated system, or XY plane, the center of the mass is,

$(x,\ y)=\left (\dfrac {m_1x_1+m_2x_2}{m_1+m_2},\ \dfrac {m_1y_1+m_2y_2}{m_1+m_2}\right)$

Then, here, the center of mass is,

$(x,\ y)=\left (\dfrac {0.5(-1)+1(3)}{0.5+1},\ \dfrac {0.5(2)+1(4)}{0.5+1}\right)\\\\\\(x,\ y)=\left (\dfrac {-0.5+3}{1.5},\ \dfrac {1+4}{1.5}\right)\\\\\\(x,\ y)=\left (\dfrac {2.5}{1.5},\ \dfrac {5}{1.5}\right)\\\\\\\mathbf {(x,\ y)=\left (\dfrac {5}{3},\ \dfrac {10}{3}\right)}$