Two discs of same mass ąnd same thickness (t) are made from two different materials of densities '…

Two discs of same mass ąnd same thickness (t) are made from two different materials of densities ' $\mathrm{d}_1$ ' and ' $\mathrm{d}_2$ ' respectively. The ratio of the moment of inertia $\mathrm{I}_1$ to $\mathrm{I}_2$ of two discs about an axis passing through the centre and perpendicular to the plane of disc is
  1. $\mathrm{d}_1: \mathrm{d}_2$
  2. $\mathrm{d}_2: \mathrm{d}_1$
  3. $1: \mathrm{d}_1 \mathrm{~d}_2$
  4. $1: \mathrm{d}_1^2 \mathrm{~d}_2$

Solution

The ratio of moments of inertia of two discs of the same mass and same thickness but of different densities is given by $\frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{\mathrm{R}_1^2}{\mathrm{R}_2^2}=\frac{\mathrm{d}_2}{\mathrm{~d}_1}$

Asked in: MHT CET 2023 (09 May Shift 1)

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