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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 ______.

Option: 1

5


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{M}_{1}=\mathrm{M}_{2}
\mathrm{~S}_{1}\left(\pi \mathrm{R}_{1}^{2} \mathrm{t}_{1}\right)=\mathrm{S}_{2}\left(\pi \mathrm{R}_{2}^{2} \mathrm{t}_{2}\right)

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

\mathrm{I}=\frac{\mathrm{MR}^{2}}{4}
\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{2}=\frac{5}{6}

Posted by

shivangi.bhatnagar

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