Having trouble finding the center of mass for multiple objects

[kavamo]

Homework Statement

Find the x-coordinate of the center of mass of the composite object shown in the figure. The sphere, cylinder, and rectangular solid all have a uniform composition. Their masses and dimensions are: sphere: 200 g, diameter = 10 cm; cylinder: 450 g, length = 11 cm, radius = 5.0 cm; rectangular solid: m = 220 g, length in x-direction = 16 cm, height = 10 cm, depth = 12 cm.

Homework Equations

using the formula: x1m1+x2m2+x3m3 / Total mass of objects

The Attempt at a Solution

200(10) + 11(450) + 16(220) / 870 = 12.0346

what am I missing/doing wrong?

 

[rock.freak667]

In the formula

$$M \bar{x}=m_1x_1+m_2x_2+m_3x_3$$

x₁,x₂ and x₃ are the centroids of the masses m₁, m₂ and m₃ respectively.

I don't think the centroid of a sphere is at the end of its diameter.

 

[kerimek]

As a scientist, it is important to remember that the center of mass is not simply the average of the individual masses and positions. It is the point at which the entire system can be balanced, taking into account the distribution of mass within each object. In this case, you will need to use the formula for finding the center of mass of a composite object, which takes into account both the position and mass of each individual object. This formula is given by xcm = (x1m1 + x2m2 + x3m3) / (m1 + m2 + m3). Additionally, make sure to convert all units to a consistent system, such as meters, before plugging them into the formula.