JEE Main 2020 · 4 September · evening · Single correct · +4 / −1

Consider two uniform discs of the same thickness and different radii R₁ = R and
R₂ = αR made of the same material. If the ratio of their moments of inertia I₁ and I₂ , respectively, about their axes is I₁ : I₂ = 1 : 16 then the value of α is :

  1. (a) √2
  2. (b) 2
  3. (c) 2√2
  4. (d) 4
Answer and solution

Answer (b) 2

Solution

Physics sir · 4 steps

Same material and same thickness means a bigger disc is also heavier, so I grows as R⁴, not R².

  1. Mass depends on R. Both discs have the same density ρ and thickness t, so the mass is M = ρ π R² t. The larger disc carries more mass.
  2. Moment of inertia. About its own axis, a uniform disc has I = 1/2MR². Substitute the mass into it.

    I = 1/2(ρ π R² t)R² = 1/2ρ π t R⁴ ⇒ I ∝ R⁴

  3. Take the ratio. I₁/I₂ = (R/(α R))⁴ = 1/α⁴ = 1/16, so α⁴ = 16.
  4. So. α = 2, which is option (b).

The idea to keep. When discs are made of the same material with the same thickness, mass scales as R². Put that into I = 1/2MR² and you get I ∝ R⁴.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 180 times in JEE Main since 2020. This question is from 2020.