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 :
Answer & explanation
Correct answer: option 1
\(\rho_1 = 7.2 gm/cc \text{ and } \rho_2 = 8.9 gm/cc\)
\(\text{As } m_1 = m_2 \text{ and } t_1 = t_2\)
\(\text{Required ratio : } \frac{I_1}{I_2} = \frac{\frac{1}{2}M_1 R^2_1}{\frac{1}{2}M_2 R^2_2} = [\frac{R_1}{R_2}]^2\)
\(\rho = \frac{m}{V} = \frac{m}{\pi R^2}\)
\(R^2 = \frac{m}{\pi \rho t}\)
\([\frac{R_1}{R_2}]^2 = \frac{\rho_2}{\rho_1}\)
Hence, \(\frac{I_1}{I_2} = \frac{\rho_2}{\rho_1} = \frac{8.9}{7.2}\)