A $5.00 \mathrm{~kg}$ mass is located at $(2.00 \mathrm{~m}, 0.00 \mathrm{~m}, 0.00 \mathrm{~m})$ and a $3.00 \mathrm{~kg}$ mass is located at $(0.00 \mathrm{~m}, 4.00 \mathrm{~m}$, $0.00 \mathrm{~m}$ ). The center of gravity of the system of masses is
A) $(1.00 \mathrm{~m}, 1.00 \mathrm{~m}, 0)$.
B) $(1.50 \mathrm{~m}, 1.25 \mathrm{~m}, 0)$.
C) $(1.25 \mathrm{~m}, 1.50 \mathrm{~m}, 0)$.
D) $(1.25 \mathrm{~m}, 1.25 \mathrm{~m}, 0)$.
E) $(1.50 \mathrm{~m}, 1.50 \mathrm{~m}, 0)$.

Question

Quizplus · Accepted Answer

The center of gravity is calculated using the formula: $(x_{cg}, y_{cg}, z_{cg}) = \left(\frac{\sum m_ix_i}{\sum m_i}, \frac{\sum m_iy_i}{\sum m_i}, \frac{\sum m_iz_i}{\sum m_i}\right)$. For the given masses, $x_{cg} = \frac{5 \times 2 + 3 \times 0}{5 + 3} = 1.25$ and $y_{cg} = \frac{5 \times 0 + 3 \times 4}{5 + 3} = 1.50$. Thus, the center of gravity is $(1.25 \mathrm{~m}, 1.50 \mathrm{~m}, 0)$.

A 5.00 kg5.00 \mathrm{~kg}5.00 kg Mass Is Located At (2.00 m,0.00 m,0.00 m)(2.00 \mathrm{~m}, 0.00 \mathrm{~m}, 0.00 \mathrm{~m})(2.00 m,0.00 m,0.00 m)

A $5.00 \mathrm{~kg}$ Mass Is Located At $(2.00 \mathrm{~m}, 0.00 \mathrm{~m}, 0.00 \mathrm{~m})$