How can we find the center of mass of a solid cone?

Nimarjeet Bajwa

Homework Statement
Find the center of mass of a solid cone taking a hollow cone as an element. given that both coens are made of same material
Homework Equations
-
is this method even possible? anyways here is my attempt

Step1) y= 2H/3 ( H is the height of the cone)

step 2) we take the density (ρ)= 3M/π R2 H.

The problem i am facing is to Find "dm"

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haruspex

Homework Helper
Gold Member
2018 Award
Homework Statement: Find the center of mass of a solid cone taking a hollow cone as an element. given that both coens are made of same material
Homework Equations: -

is this method even possible?
Yes.
Consider a nested stack of hollow conical shells each of thickness dr. Find the mass and mass centre of each (measured from the common base).

Nimarjeet Bajwa

Yes.
Consider a nested stack of hollow conical shells each of thickness dr. Find the mass and mass centre of each (measured from the common base).
should we also take a height of every hollow cone as "dh" ?

haruspex

Homework Helper
Gold Member
2018 Award
should we also take a height of every hollow cone as "dh" ?
The heights will not be infinitesimals, so dh would be inappropriate.
If the radius of one of these hollow cones is r, what is its height?

"How can we find the center of mass of a solid cone?"

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