Center of mass of a two rod system

[schaafde]

Homework Statement

Given that I have a system with a rod of diameter 1 1/2 inches with a length of 17 in and a weight of 10 1/3 oz and a rod with a diameter of 3 inches with a length of 17 in and a weight of 20 2/3 oz. The two rods are butted together at one end almost looking like a bottle. What is the center of mass of the system?

Homework Equations

Center of mass = 1/M Ʃ miri

The Attempt at a Solution

I calculated the center of mass of each rod for the thinner,lighter rod the center of mass is in the middle of that rod. For the thicker,heavier rod the center of mass is in the middle. I calculated the center of mass to be 2/3 of the way of the entire 34 inches from the thinner rod since the heavier rod carries 2/3 of the weight of the system. Would I be correct in saying that the center of mass of the system is 5 2/3 of the way into the bigger rod?

 

[NascentOxygen]

Show your calculation, so we can check that you have done this correctly.