A 30.0 g mass is located at the origin. Where must a mass of 10.0 g be located if the coordinates of the center of mass are (0.00 cm, 10.0 cm)?
A) (0.00 cm, 5.00 cm)
B) (0.00 cm, 7.50 cm)
C) (0.00 cm, 10.0 cm)
D) (0.00 cm, 20.0 cm)
E) (0.00 cm, 40.0 cm)

Question

Quizplus · Accepted Answer

The center of mass (CM) can be calculated using the formula: $$CM = \frac{\sum m_ix_i}{\sum m_i}$$ where $m_i$ and $x_i$ are the masses and their respective positions. Given the CM is at (0, 10) and one mass is at the origin (0,0), we solve for the position of the 10.0 g mass. Let $x$ be the position of the 10.0 g mass. Setting up the equation: $$10 = \frac{(30.0 \times 0) + (10.0 \times x)}{30.0 + 10.0}$$ Simplifying, we find $x = 40$ cm, meaning the 10.0 g mass must be placed at (0.00 cm, 40.0 cm) to achieve the given center of mass.

A 300 G Mass Is Located at the Origin