Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm respectively. The densities of the materials are in the ratio 3 : 5. The moment of inertia of these discs respectively about their d

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Solution

Q.
Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0.5 cm respectively. The densities of the materials are in the ratio 3 : 5. The moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$ . The value of $x$ is ________. [2023]

Ans.
(5)

$m = ρ π R^{2} t$

$So R^{2} = \frac{m}{ρ π t}$

$I = \frac{m R^{2}}{4} = \frac{m^{2}}{4 ρ π t}$

$So \frac{I_{1}}{I_{2}} = \frac{ρ_{2} t_{2}}{ρ_{1} t_{1}} = \frac{5}{3} \times \frac{0.5}{1} = \frac{5}{6}$

$So x = 5$

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