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  • The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is  to the plane of the disc and pa

The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is \perp to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)
Option: 1 R^{2}: r^{2}
Option: 2 2 r^{4}: R^{4}
Option: 3 2 R^{2}: r^{2}
Option: 4 2 R^{4}: r^{4}

Answers (1)

best_answer

I_{1}=\frac{M_{1} R^{2}}{2}

I_{1}\rightarrow Moment of inertia of larger disc about AB

I_{2}=\frac{M_{2}r^{2}}{4}

I_{2}\rightarrow Moment of inertia of smaller disc around one of its diameter.

\frac{I_{1}}{I_{2}}=\frac{M_1R^{2} / 2}{\frac{M_{2} r^{2}}{4}}

\begin{gathered} \frac{M_{1}}{\pi R^{2}}=(k)=\frac{M_{2}}{\pi r^{2}} \\ \frac{M_{1}}{M_{2}}=\frac{R^{2}}{r^{2}} \end{gathered}

\frac{I_{1}}{I_{2}}=\frac{ 2 R^{4}}{r^{4}}

The correct option is (4).

Posted by

vishal kumar

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