Three point masses of 2 kg, 3 kg and 15 kg are placed at the vertices shown in the figure. Point P, the midpoint of the perpendicular bisector indicated in the figure, is taken as the origin. What are the coordinates of the centre of mass of the three-particle system?

Question

G1 Physics · Accepted Answer

Using P as the origin and the geometry shown in the figure, the coordinates of the masses can be written as 2 kg: (-5√3, -5 ÷ 2), 3 kg: (5√3, -5 ÷ 2), 15 kg: (0, 5 ÷ 2). Total mass: M = 2+3+15 = 20 kg. The x-coordinate of the centre of mass is x(cm) = [2(-5√3)+3(5√3)+15(0)] ÷ 20 = 5√3 ÷ 20 = √3 ÷ 4. The y-coordinate is y(cm) = [2(-5 ÷ 2)+3(-5 ÷ 2)+15(5 ÷ 2)] ÷ 20 = 25 ÷ 20 = 1.25. Therefore the centre of mass is (√3 ÷ 4, 1.25). Correct option: A.