Question

Two solid spheres of the same mass are made of metals of different densities. which of them has larger moment of inertia about its diameter?

Answer 1

The sphere with larger.moment of inertia will be the one having lower density.

•Moment of inertia is defined as "a rotating body's resistance to angular acceleration or deceleration."

•Moment of inertia is given by the formula - summation of (m*r²).

•M is mass, r is radius.

•Now, density is given by the formula - density = mass/volume.

•Further, formula for volume is 4/3πr³.

•This formula indicates that density is inversely proportional to radius.

•Thus, lower density means larger radius.

•Larger radius in turn indicates larger moment of inertia.

•Hence, sphere with less density and large radius will have more moment of inertia.

Answer 2

The metal with lower density will have larger moment than the other one.

Explanation:

• Two different metals of different densities are used to make two squares and we need to know about the moment of inertia each square will possess.
• Then we need to go through the formula that moment of inertia  who is calculated from which shows the dependency of Moment of inetia on mass and radius and we also know that it is related to density because density can be found out using quotient of mass and volume.
• So seeing both the formulas we can conclude that Moment of inetia will inversely depends on density.
• Hence, the metals sphere that has a density less than the other one will have Moment of Inertia more than the other sphere.

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Two solid spheres of same mass are made of metals of different densities.Which of them has larger moment of inertia about it's diameter?

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