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31 January, 20:46

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

+2
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  1. 31 January, 20:49
    0
    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.
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