Calculate the x-coordinate of the center of mass for two point masses: m1 = 2 kg at x1 = 0 m, m2 = 3 kg at x2 = 4 m.

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Multiple Choice

Calculate the x-coordinate of the center of mass for two point masses: m1 = 2 kg at x1 = 0 m, m2 = 3 kg at x2 = 4 m.

Explanation:
The x-coordinate of the center of mass on a line is the weighted average of the positions, using the masses as weights. So you use x_cm = (m1 x1 + m2 x2) / (m1 + m2). Plugging in the values: m1 x1 = 2 kg × 0 m = 0, m2 x2 = 3 kg × 4 m = 12, total mass = 2 kg + 3 kg = 5 kg. Thus x_cm = 12 / 5 = 2.4 m. This value lies between the two positions and is pulled toward the heavier mass at x = 4 m, which matches the intuition of a weighted average.

The x-coordinate of the center of mass on a line is the weighted average of the positions, using the masses as weights. So you use x_cm = (m1 x1 + m2 x2) / (m1 + m2).

Plugging in the values: m1 x1 = 2 kg × 0 m = 0, m2 x2 = 3 kg × 4 m = 12, total mass = 2 kg + 3 kg = 5 kg. Thus x_cm = 12 / 5 = 2.4 m.

This value lies between the two positions and is pulled toward the heavier mass at x = 4 m, which matches the intuition of a weighted average.

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