Two discs,one of density 7.2 , g/cm^3 and the | vedclass

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(A) The moment of inertia of a disc about its central axis is given by $I = \frac{1}{2} M r^2$.Since the mass $M$ and thickness $t$ are the same for b

Vedclass · Accepted Answer

$\frac{8.9}{7.2}$

Vedclass · Answer

(A) The moment of inertia of a disc about its central axis is given by $I = \frac{1}{2} M r^2$.Since the mass $M$ and thickness $t$ are the same for both discs,we relate mass to density $\rho$ and radius $r$ as $M = \rho \cdot V = \rho \cdot (\pi r^2 t)$.Since $M$ and $t$ are constant,$\rho_1 r_1^2 = \rho_2 r_2^2$,which implies $\frac{r_1^2}{r_2^2} = \frac{\rho_2}{\rho_1}$.The ratio of the moments of inertia is $\frac{I_1}{I_2} = \frac{\frac{1}{2} M r_1^2}{\frac{1}{2} M r_2^2} = \frac{r_1^2}{r_2^2}$.Substituting the density ratio,we get $\frac{I_1}{I_2} = \frac{\rho_2}{\rho_1} = \frac{8.9}{7.2}$.

Two discs,one of density $7.2 \, g/cm^3$ and the other of density $8.9 \, g/cm^3$,have the same mass and thickness. What is the ratio of their moments of inertia?

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