Centroid - two bodies

A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravity of this body system.

Correct result:

T =  0.733 m

Solution:

$l=0.8 \ \text{m} \ \\ r=0.1 \ \text{m} \ \\ m_{1}=1 \ \\ m_{2}=2 \ \\ \ \\ t_{1}=l/2=0.8/2=\dfrac{ 2 }{ 5 }=0.4 \ \text{m} \ \\ t_{2}=l+r=0.8+0.1=\dfrac{ 9 }{ 10 }=0.9 \ \text{m} \ \\ \ \\ T=\dfrac{ t_{1} \cdot \ m_{1} + t_{2} \cdot \ m_{2} }{ m_{1}+m_{2} }=\dfrac{ 0.4 \cdot \ 1 + 0.9 \cdot \ 2 }{ 1+2 }=\dfrac{ 11 }{ 15 }=0.733 \ \text{m}$

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