Formula of object immersed in water

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werson tan
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Homework Statement


why the y ſ P dA will equal to P yc A ? why not P (yc^2) A ? since yc = ſ y dA / A

Homework Equations

The Attempt at a Solution

 

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haruspex said:
It comes from the definition of yc at 3-18.
according to 3-18 , i would get P (yc^2) A instead of P (yc) A ... am i correct ?
 
werson tan said:
according to 3-18 , i would get P (yc^2) A instead of P (yc) A ... am i correct ?
No.
3-18 defines ##y_c=\frac 1A\int_AydA##. So at 3-20, ##P_0\int_AydA=P_0Ay_c##.
How do you get yc2 terms?
 
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