(C) The moment of inertia $I$ of a solid sphere of mass $M$ and radius $R$ about its diameter is given by $I = \frac{2}{5} M R^2$. Since the mass $M$

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(C) The moment of inertia $I$ of a solid sphere of mass $M$ and radius $R$ about its diameter is given by $I = \frac{2}{5} M R^2$. Since the mass $M$ is the product of volume $V$ and density $\rho$, we have $M = V \rho = \frac{4}{3} \pi R^3 \rho$. Substituting this into the formula for $I$, we get $I = \frac{2}{5} (\frac{4}{3} \pi R^3 \rho) R^2 = \frac{8}{15} \pi R^5 \rho$. Therefore, the ratio of the moments of inertia is $\frac{I_A}{I_B} = \frac{\frac{8}{15} \pi R^5 \rho_A}{\frac{8}{15} \pi R^5 \rho_B} = \frac{\rho_A}{\rho_B}$.

Class 11 Physics System of Particles and Rotational Motion Moment of Inertia and Radius of gyration

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Two solid spheres $A$ and $B$ each of radius $R$ are made of materials of densities $\rho_A$ and $\rho_B$ respectively. Their moments of inertia about a diameter are $I_A$ and $I_B$ respectively. The value of $\frac{I_A}{I_B}$ is

TS EAMCET 2012 All TS EAMCET

A
$\sqrt{\frac{\rho_A}{\rho_B}}$
B
$\sqrt{\frac{\rho_B}{\rho_A}}$
C
$\frac{\rho_A}{\rho_B}$
D
$\frac{\rho_B}{\rho_A}$

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Moment of Inertia and Radius of gyration

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Two solid spheres $A$ and $B$ each of radius $R$ are made of materials of densities $\rho_A$ and $\rho_B$ respectively. Their moments of inertia about a diameter are $I_A$ and $I_B$ respectively. The value of $\frac{I_A}{I_B}$ is

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