Calculation of center of mass difficult

[eileen6a]

Homework Statement

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Homework Equations

integration

The Attempt at a Solution

a) i use surface density and calculate the mass of a disk and integrate it from bottom to top. Is it right? But the cone is hollow so i only need to use the mass of the circuference?
b) use "negative mass"? are there any other approaches?
c) is it just a simplification of part a)?
thx!

 

[vela]

It would help if you provided the actual problem.

 

[eileen6a]

i think some removed it?uploaded again as attached

 

[vela]

a) i use surface density and calculate the mass of a disk and integrate it from bottom to top. Is it right? But the cone is hollow so i only need to use the mass of the circuference?

In part a, the cone is a solid, not hollow, so you want to use the volume density ρ=m/V, where m is the mass of the cone and V is its volume.

Can you write down the integral to calculate the volume of the cone? That's a good starting point.

b) use "negative mass"? are there any other approaches?
c) is it just a simplification of part a)?
thx!

For part c, it's not quite a simplification. This time you do want to use the surface density σ=m/A, where A is the surface area of the cone, and setting up the integral is a bit different.

It would help if you show us your calculations.