A $2.00 \mathrm{~kg}$ mass is located at $(4.00 \mathrm{~m}, 0.00 \mathrm{~m}, 0.00 \mathrm{~m})$ and a $4.00 \mathrm{~kg}$ mass is located at $(0.00 \mathrm{~m}, 3.00 \mathrm{~m}$, $0.00 \mathrm{~m}$ ). The center of gravity of the system of masses is
A) $(1.33 \mathrm{~m}, 2.00 \mathrm{~m}, 0)$.
B) $(1.33 \mathrm{~m}, 1.00 \mathrm{~m}, 0)$.
C) $(2.00 \mathrm{~m}, 1.33 \mathrm{~m}, 0)$.
D) $(1.50 \mathrm{~m}, 1.33 \mathrm{~m}, 0)$.
E) $(1.33 \mathrm{~m}, 1.50 \mathrm{~m}, 0)$.

Question

Quizplus · Accepted Answer

The center of gravity (CG) can be calculated using the formula $\text{CG} = \frac{\sum m_i x_i}{\sum m_i}$ for each dimension (x, y, z). For the x-coordinate: CG_x = $\frac{(2 \times 4) + (4 \times 0)}{2 + 4} = \frac{8}{6} = 1.33 \, \text{m}$. For the y-coordinate: CG_y = $\frac{(2 \times 0) + (4 \times 3)}{2 + 4} = \frac{12}{6} = 2.00 \, \text{m}$. The z-coordinate is 0 since all masses are in the x-y plane. Therefore, the center of gravity is at $(1.33 \, \text{m}, 2.00 \, \text{m}, 0)$.

A 2.00 kg2.00 \mathrm{~kg}2.00 kg Mass Is Located At (4.00 m,0.00 m,0.00 m)(4.00 \mathrm{~m}, 0.00 \mathrm{~m}, 0.00 \mathrm{~m})(4.00 m,0.00 m,0.00 m)

A $2.00 \mathrm{~kg}$ Mass Is Located At $(4.00 \mathrm{~m}, 0.00 \mathrm{~m}, 0.00 \mathrm{~m})$