Comparing Moment of Inertia of Wood and Iron Spheres

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Homework Help Overview

The discussion revolves around comparing the moment of inertia of two spherical objects, one made of wood and the other made of iron, both having the same diameter. Participants are exploring the implications of mass differences on moment of inertia.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are examining the relationship between mass and moment of inertia, particularly questioning how the mass of the iron sphere, being greater than that of the wooden sphere, affects their respective moments of inertia. There is a specific focus on the formula for solid spheres and its application to both materials.

Discussion Status

The discussion includes attempts to apply the moment of inertia formula to both spheres, with one participant suggesting that the greater mass of the iron sphere should lead to a larger moment of inertia. However, the conversation does not reach a consensus, as another participant implies that the question has been resolved.

Contextual Notes

There is an assumption that both spheres have the same radius, and the mass of the iron sphere is stated to be twice that of the wooden sphere. The discussion is framed within the context of a homework question, which may impose certain constraints on the exploration of the topic.

Amith2006
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Sir,
1) Consider two spherical balls one made of wood and other made of iron having the same diametre. Which one has greater moment of inertia about their centre of gravity?
 
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The formula for any solid sphere is
[tex]I=\frac{2}{5}mr^2[/tex]
 
Sir,
My doubt is - For a given radius, the iron sphere having a greater mass should have larger moment of inertia, isn't it?Suppose mass of iron sphere is twice the mass of wooden sphere. In that case,
Moment of inertia of wooden ball = 2/5(MR^2)
Moment of inertia of iron ball = 2/5(2MR^2)
Here the symbol "^" represents power.
 
You got your answer...
 

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