Two circular discs A and B are of equal masses and thickness but made

Question

Two circular discs A and B are of equal masses and thickness but made of metals with densities

d_{A}

and

d_{B} (d_{A} > d_{B}) .

If their moments of inertia about an axis passing through centres and normal to the circular faces be

I_{A}

and

I_{B}

, then

Options:

A . IA=IB

B . IA>IB

C . IA

D . IA>=

Answer: Option C
:
C
Moment of inertia of circular disc about an axis passing through centre and normal to the circular face

I = \frac{1}{2} M R^{2} = \frac{1}{2} M (\frac{M}{π t ρ})

[A s M = V ρ = π R^{2} t ρ ∴ R^{2} = \frac{M}{π t ρ}]

\Rightarrow I = \frac{M^{2}}{2 π t ρ}

I \propto \frac{1}{ρ}

If mass and thickness are constant.
So, in the problem

\frac{I_{A}}{I_{B}} = \frac{d_{B}}{d_{A}}

∴ I_{A} < I_{B}

[A s d_{A} > d_{B}]

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