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A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia I_A and I_B is

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I_A < I_B

Depends on the actual values of t and r.

I_A = I_B

I_A > I_B

answer is C.

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Detailed Solution

For a solid disc ,

I = 1/2 mR²

m = π R² / t ρ , where ρ = Density

.: I = 1/2 (πR² + σ) R²

⇒ I $\large \propto$ t R⁴

.: I_A = I_B = (t / t/4) (r / 4r)⁴ = 1/64

.: I_A < I_B

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