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.

Options

A. `(0.5,0.3)`
B. `(0.4,0.3)`
C. `(0.5,0.8)`
D. `(0.7,0.3)`

Answer

A

Explanation

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 COM are
`x_(COM)=(m_1x_1+m_2x_2+m_3x_3+m_4x_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=0.5m`
Similarly, `y_(COM)=(m_1y_1+m_2y_2+m_3y_3+m_4y_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`
`:. (x_(COM), y_(COM))=(0.5m, 0.3m)`
Thus, position of COM of the four particles is as shown in fig.