Three masses are positioned along the x-axis.Their masses and positions are m₁ = m with x₁ = 1.0 m,m₂ = 2m with x₂ = 2.0 m,and m₃ = 9.0m with x₃ = 3.0 m.What is the x-coordinate of the center of mass of this system,to the nearest tenth? A)4.7 m B)2.7 m C)2.0 m D)0.7 m E)Not enough information

Question

Quizplus · Accepted Answer

The x-coordinate of the center of mass, Xcm, is given by:

Xcm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)

Plugging in the values given:

Xcm = ((1.0 m)*(1.0 m) + (2.0 m)*(2.0 m) + (9.0 m)*(3.0 m)) / (1.0 m + 2.0 m + 9.0 m)

Xcm = (1.0 m + 4.0 m + 27.0 m) / 12.0 m

Xcm = 32.0 m / 12.0 m

Xcm ≈ 2.7 m

Therefore, the answer is B.

Three Masses Are Positioned Along the X-Axis