Question

Three blocks of uniform thickness and masses `m, m and 2m` are placed at the corners of a triangle having co-ordinates `(2.5, 1.5),(3.5,1.5) and (3,3)` respectively. Find the co-ordinates of the centre of mass of the system.

Answer 1

Here, `m_(1) = m,m_(2) =m, m_(3) = 2m`
`x_(1) = 2.5, x_(2) = 3.5, x_(3) = 3`,
`y_(1) = 1.5, y_(2) = 3.5, y_(3) = 3`.
`:. x_(cm) = (m_(1)x_(1) + m_(2)x_(2) + m_(3)x_(3))/(m_(1)+ m_(2) + m_(3))`
`= (m xx 2.5 + mxx3.5 + 2m xx 3)/(m + m + 2m) = 3`
`y_(cm) = (m_(1)y_(1) + m_(2)y_(2) + m_(3)y_(3))/(m_(1)+ m_(2) + m_(3))`
`= (m xx 1.5 + m xx 1.5 + 2m xx 3)/(m + m + 2m) = 2.25`