Is it always true that a solid object(geometrical figure) has less moment of inertia than its corresponding hollow one?

Question

what I mean is that,if you have two objects(one hollow and other solid):

Lets say, a solid sphere and a hollow sphere and if you calculate moment of inertia of the two of them, you would find that moment of inertia is more in the hollow one than in the solid one.

So, is this concept i.e moment of inertia of a hollow object is more than its corresponding solid one always true?

Given:mass of both the bodies are equal

NOTE:THIS ISN'T A DUPLICATE QUESTION,ALL THE PREVIOUS QUESTION EXPLAIN IT FOR A PARTICULAR BODY ,BUT I'M QUESTIONING ITS VALIDITY FOR EVERYTHING(UNIVERSAL OR NOT)

Answer 1

That is not always true.

Consider the following figures:

Let us assume that this is a section of a cylindrical shape that stretches along the third dimension long enough that the effects of bottom and top are negligible for the overall moment.

We see that most of the mass of hollow shape is concentrated in the star-shaped curve which has a relatively small average distance from the center. While for the solid shape the average distance would be larger.

By simultaneously increasing the number of rays in the star and radius of outer circle (and keeping the overall mass the same) we can make the ratio $I_\text{solid}/I_\text{hollow}$ arbitrary high.

Answer 2

It is always true and you can understand why from the physical interpretation of moment of inertia. It is a measure of how easily you can rotate an object in the same sense that the mass is a measure of how easily you can move an object. After all, the moment of inertia is the precise analogue of the mass for rotational motion.

And it is not hard to convince yourself that the further from the center of mass a mass is distributed, the harder it is to rotate it just like the heavier an object is, the harder it is to move it. Therefore, since any hollow geometrical object is always harder to rotate than its equal mass compact analogue, its moment of inertia is always bigger.

Hope this makes things more intuitive for you.