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

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.