Three particles are placed in the xy-plane. A 30 g particle is located at (3 m, 4 m), and a 40 g particle is located at (2 m, 2 m).

Where must a 20 g particle be placed so that the center of mass of the three-particle system is at the origin, (0 m, 0 m) ?

a) (-3, - 1) m

b) (+1, + 3) m

c) (-0.5, - 2) m

d) (+3, - 1) m

Answer:cles the formula is as follows

x coordinate of CM = (m₁x₁ + m₂x₂ + m₃x₃) / (m₁ + m₂ + m₃)

m₁, m₂, m₃ are three masses and x₁, x₂ and x₃ are their x coordinates.

Putting the given data

0 = (30 x 3 + 40 x 2 + 20 x x₃) / 30 + 40 + 20

0 = 90 + 80 + 20 x₃ / 90

20 x₃ = - 170

x ₃ = - 8.5 cm

Similarly, to obtain y axis

y coordinate of CM = (m₁y₁ + m₂y₂ + m₃y₃) / (m₁ + m₂ + m₃)

0 = (30 x 4 + 40 x 2 + 20 x y₃) / 30 + 40 + 20

0 = 120 + 80 + 20 y₃ / 90

20 y₃ = - 200

y ₃ = - 10 cm

No alternative correct.