Determine the x-coordinate of the mass center of the homogeneous hemisphere

[Godblessyou]

Homework Statement

Determine the x-coordinate of the mass center of the homogeneous hemisphere with the smaller hemispherical portion removed?

I know what the answer should be it's Xcm = 45/112 R

Homework Equations

The center of mass R of a system of particles is defined as the average of their positions, ri, weighted by their masses, mi

The Attempt at a Solution

dm = pi*p*(R^2 - x^2)
and then doing the (integral of x*(dm/dx)*dx)/integral from 0 to R (dm/dx)*dx
which finally gives me 3/2R but this is wrong. Please someone help thanks

 

[berkeman]

Homework Statement

Determine the x-coordinate of the mass center of the homogeneous hemisphere with the smaller hemispherical portion removed?

I know what the answer should be it's Xcm = 45/112 R

Homework Equations

The center of mass R of a system of particles is defined as the average of their positions, ri, weighted by their masses, mi

The Attempt at a Solution

dm = pi*p*(R^2 - x^2)
and then doing the (integral of x*(dm/dx)*dx)/integral from 0 to R (dm/dx)*dx
which finally gives me 3/2R but this is wrong. Please someone help thanks

It's a little hard to tell without the integral in Latex notation, but did you remember to remove the smaller hemisphere? Why is your integration from 0 to R? And why isn't it a triple integral?

 

[Godblessyou]

Yes I did remove smaller hemisphere from bigger which gave me 3/2R. I don't understand what you mean and what you are asking?

 

[berkeman]

Yes I did remove smaller hemisphere from bigger which gave me 3/2R. I don't understand what you mean and what you are asking?

I mentioned Latex to help you post your equations in a format that is more readable. Look at the Latex Tutorial thread in the Learning Materials area of the PF:

https://www.physicsforums.com/forumdisplay.php?f=151

I mentioned the triple integral, because what you wrote looks like a 1-D integration, and it would seem that you need to integrate over the volume of the object, no?