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

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Homework Help Overview

The discussion revolves around finding the center of mass of a solid cone, with participants exploring various methods and considerations related to the problem. The subject area includes concepts from calculus and physics, particularly in relation to mass distribution and geometry.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the feasibility of using a method involving hollow conical shells to determine the center of mass. There are attempts to define the mass element "dm" and questions about the appropriate dimensions for the hollow cones, such as height and thickness.

Discussion Status

The discussion is active, with participants providing insights into the method of using hollow conical shells. Some guidance has been offered regarding the mass and mass center of these shells, while questions about the appropriateness of certain variables, like the height of the hollow cones, are being explored.

Contextual Notes

There is a mention of the assumption that both the solid cone and the hollow cone elements are made of the same material, which may influence the density calculations. Additionally, the heights of the hollow cones are noted to not be infinitesimal, raising questions about the definitions being used.

Nimarjeet Bajwa
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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
Relevant 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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Nimarjeet Bajwa said:
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).
 
haruspex said:
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" ?
 
Nimarjeet Bajwa said:
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?
 

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