JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Rotational Mechanics

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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 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 ____.

Answer: 5

Solution

About a diameter each disc has moment of inertia

\frac{1}{4} m R^{2}

, so with equal masses the ratio depends only on the radii,

\frac{I _{1}}{I _{2}} = \frac{R _{1}^{2}}{R _{2}^{2}}

. The common mass is

m = ρ π R^{2} t

, and equating the two masses gives

ρ_{1} R_{1}^{2} t_{1} = ρ_{2} R_{2}^{2} t_{2}

, so

\frac{R _{1}^{2}}{R _{2}^{2}} = \frac{ρ _{2} t _{2}}{ρ _{1} t _{1}} = \frac{5 \times 0.5}{3 \times 1} = \frac{5}{6}

. The moments of inertia are in the ratio

\frac{5}{6}

, and matching this to

\frac{x}{6}

gives

x = 5

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer

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JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Rotational Mechanics

Solution

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