# Step-by-Step Solution ## Step 1: Find the Center of Mass Let's assign the mass and coordinates to each colored dot from the image: | Dot | Mass (kg) | x-coordinate | y-coordinate | |-----|-----------|--------------|--------------| | A | 2 | 1 | 4 | | B | 5 | 3 | 3 | | C | 10 | 2 | 1 | | D | 8 | 7 | 4 | ### Center of Mass Formula For \( n \) particles at positions \((x_i, y_i)\) with masses \(m_i\): \[ x_{cm} = \frac{\sum m_i x_i}{\sum m_i} \] \[ y_{cm} = \frac{\sum m_i y_i}{\sum m_i} \] **Calculate the total mass:** \[ M = 2 + 5 + 10 + 8 = 25 \text{ kg} \] **Calculate \(x_{cm}\):** \[ x_{cm} = \frac{(2 \times 1) + (5 \times 3) + (10 \times 2) + (8 \times 7)}{25} = \frac{2 + 15 + 20 + 56}{25} = \frac{93}{25} = 3.72 \] **Calculate \(y_{cm}\):** \[ y_{cm} = \frac{(2 \times 4) + (5 \times 3) + (10 \times 1) + (8 \times 4)}{25} = \frac{8 + 15 + 10 + 32}{25} = \frac{65}{25} = 2.6 \] **Explanation:** - Each mass's x and y coordinate is multiplied by its mass, summed, and divided by the total mass to get the center of mass. --- ## Step 2: Locate the Center of Mass in the Figure - The center of mass is at \((x_{cm}, y_{cm}) = (3.72, 2.6)\) - On the figure, this point would be a little to the right of the red dot (x=3) and slightly above the halfway point between y=2 and y=3. --- ## Final Answer **The center of mass of the system is at \((3.72, 2.6)\).** This is where you would mark the center of mass in the figure. --- **Let me know if you want the solutions for parts (a), (b), or (c) as mentioned in your problem statement!**