Practicing Success
Two disc one of the density 7.2 gm/cc and other of density 8.9 gm/cc are of the same mass and thickness their moment of inertia are in the ratio of : |
8.9 : 7.2 7.2 : 8.9 1 : 64 64 : 1 |
8.9 : 7.2 |
\(\rho_1 = 7.2 gm/cc \text{ and } \rho_2 = 8.9 gm/cc\) \(\text{As } m_1 = m_2 \text{ and } t_1 = t_2\) \(\text{Required ratio : } \frac{I_1}{I_2} = \frac{\frac{1}{2}M_1 R^2_1}{\frac{1}{2}M_2 R^2_2} = [\frac{R_1}{R_2}]^2\) \(\rho = \frac{m}{V} = \frac{m}{\pi R^2}\) \(R^2 = \frac{m}{\pi \rho t}\) \([\frac{R_1}{R_2}]^2 = \frac{\rho_2}{\rho_1}\) Hence, \(\frac{I_1}{I_2} = \frac{\rho_2}{\rho_1} = \frac{8.9}{7.2}\) |