Question

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.

Answer 1

Assuming D as the origin, DC as X-axis and DA as Y-axis, we have
`m_(1) = 1kg, (x_(1)-y_(1))=(0,1m)`
`m_(2) = 2kg, (x_(2),y_(2))=(1m,1m)`
`m_(3) = 3kg, (x_(3), y_(3)) = (1m,0)`
and `m_(4) = 4kg, (x_(4),y_(4)) = (0,0)`
Coordinates 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) = 5/10=1/2m = 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(1) +2(1)+3(0)+4(0))/(1+2+3+4) = 3/10m = 0.3m`
`therefore` Center of mass is at(x_(CM),y_(CM)) = (0.5m, 0.3m) = 0.3m)