QJEEM23Phc6d3: JEE Main 2023 Physics - Class 11 JEEM23Phc6d3 Solution: Two discs of same mass and different radii are made of…

Question

Verified Solution • 2025–26 Session moderate

Two discs of same mass and different radii are made of different materials such that their thicknesses are

1 \mathrm{~cm}

and

0.5 \mathrm{~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 ________.

Accepted Answer

m=\rho \pi R^{2} t

\begin{aligned}&amp; \text { so } R^{2}=\frac{m}{\rho \pi t} \\\\&amp; I=\frac{m R^{2}}{4}=\frac{m^{2}}{4 \rho \pi t}\end{aligned}

So

\frac{I_{1}}{I_{2}}=\frac{\rho_{2} t_{2}}{\rho_{1} t_{1}}=\frac{5}{3} \times \frac{0.5}{1}=\frac{5}{6}

So

x=5

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