The center of mass of a two-particle system is at the origin.One particle is located at (3.0 m,0.0 m)and has a mass of 2.0 kg.The other particle has a mass of 3.0 kg.What is the location of the 3.0-kg particle?
A)(-3.0 m, 0.0 m)
B)(-2.0 m, 0.0 m)
C)(2.0 m, 0.0 m)
D)(3.0 m, 0.0 m)

Question

Quizplus · Accepted Answer

The center of mass formula for a two-particle system is:

r_cm = (m1r1 + m2r2) / (m1 + m2)

Given that the center of mass is at the origin, we can write:

(m1r1 + m2r2) / (m1 + m2) = 0

Substituting the values:

(2.0 kg)(3.0 m) + (3.0 kg)(r2) = 0

6.0 + 3r2 = 0

r2 = -2.0 m

Therefore, the location of the 3.0 kg particle is (-2.0 m, 0.0 m), which corresponds to choice B.

The Center of Mass of a Two-Particle System Is at the Origin.One