Finding the y Component of the Centroid: Is My Reasoning Valid?

[Miike012]

The test question was...
We are given a region bounded by the functions √x and x. We were also given the density and mass of the region and asked to only the component y of the centroid.

I did not know how to implement these given variables, density and mass into my equation for y bar so I found y bar by integrating the moment about x over total mass.

Is my reasoning valid... the y component of the centroid of the bounded region does not depend on the value of rho or mass given because if density is dispersed evenly through out the region (which it is or atleast it should be from what the book says) then y bar will be at the same location always. The only time it would move is if the density or mass was shifted.

 

[genericusrnme]

Are you sure you were asked for the centroid?
The centroid is the 'geometric center' it doesn't depend on mass density at all.

If it's the center of mass then, you'll have to refresh my memory here, moment is used to describe pretty much everything so I'm not quite sure what you mean by moment, nor do I know what you mean by y bar.

Imagine a group of discrete objects of equal mass, how would their density and total mass change the value of the center of mass?

If it was the centroid then the density doesn't play a role at all and indeed the y coordinate of the centroid would be independant of the density.