Q 11-06-019NEETJEE MainEAMCET 2007 (Engineering)Medium
Two solid spheres A and B are made of metals of different densities $\rho_A$ and $\rho_B$ respectively. If their masses are equal, the ratio of their moments of inertia $\dfrac{I_A}{I_B}$ about their respective diameters is
Answer: (A) $\left(\dfrac{\rho_B}{\rho_A}\right)^{2/3}$
Equal masses: $\dfrac{4}{3}\pi R_A^3\rho_A = \dfrac{4}{3}\pi R_B^3\rho_B$, so $\dfrac{R_A}{R_B} = \left(\dfrac{\rho_B}{\rho_A}\right)^{1/3}$.
$I = \dfrac{2}{5}mR^2$ with equal $m$:
$$\frac{I_A}{I_B} = \left(\frac{R_A}{R_B}\right)^2 = \left(\frac{\rho_B}{\rho_A}\right)^{2/3}$$
Solution by Sreeraj P, M.Sc Physics