Question

Ratio of densities of materials of two circular discs of same mass and thickness is5:6.Ratio of their moment of inertia about their natural axes is

Answer 1

Answer:

5:6 is the answer

believe this

Answer 2

Concept:

The moment of inertia can be defined as the product of mass and square of the radius of the disc.

Given:

The ratio of the density of materials 1 and 2 is 5:6, and the mass and thickness of the discs are the same.

Find:

The ratio of the moment of inertia about their natural axes.

Solution:

As given the ratio of the densities of the materials is 5:6,

So, taking any proportionality constant p, this results in the density of material 1 in d₁ = 5p and density of material 2 in d₂ = 6p.

The masses of the discs are the same:

So, M = M₁ = M₂

As mass can be represented as the product of density and volume,

πR₁²d₁ = πR₂²d₂

πR₁²5p = πR₂²6p

R₁²/R₂² = 6/5

Moment of inertia about their axes can be given as:

I₁ = MR₁²

I₂ = MR₂²

I₁ / I₂ = MR₁² / MR₂²= R₁²/R₂²

I₁ / I₂ = 6/5

Hence, the ratio of their moment of inertia about their natural axes is 6:5, when the mass and thickness are identical, and the ratio of densities of the materials is 5:6.

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