Four particles of masses 1kg, 2kg, 3kg and 4kg are placed at the four vertices A, B, C and D of a square of side 1m. Find the position of centre of mass of the particles. Assume that D is situated at the origin.

Explanation

Assuming A as the origin, AB as x-axis and AD as y-axis we have
Mass of first particle, `m_(1)` = 1kg , Mass of second particle, `m_(2)` = 2kg
Mass of third particle, `m_3 = 3kg` ,
Mass of fourth particle, `m_4 = 4`kg
Co - ordinates of first particle, (`x_(1),y_(1)`)= (0,0)
Co - ordinates of second particle, `(x_2, y_2)` = (1,0)
Co - ordinates of third particle `(x_3,y_3) = (1,1)`
Co - ordinates of fourth particle `(x_4,y_4) = (0,1)`
Co-ordinates of their CM are:

`x_(CM) =(m_(1)x_(1) + m_(2)x_(2) + m_(3)x_(3) + m_(4)x_(4))/(m_(1) + m_(2) +m_(3) + m_(4)) =((1)(0)+2(1) + 3(1) + 4(0))/(1+2+3+4)=0.5 m`
Similarly, `y_(CM) =(m_(1)y_(1) + m_(2)y_(2) + m_(3)y_(3) + m_(4)y_(4))/(m_(1)+m_(2)+m_(3)+m_(4)) =(1(0) + 2(0) + 3(1) + 4(1))/(1+2+3+4) =0.7 m`
`therefore` Co-ordinates of centre of mass `(x_(cm),y_(cm)) =(0.5 m, 0.7 m)`