Practicing Success

Target Exam

CUET

Subject

Physics

Chapter

System of Particle and Rotational Motion

Question:

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 : 

Options:

8.9 : 7.2

7.2 : 8.9

1 : 64

64 : 1

Correct Answer:

8.9 : 7.2

Explanation:

\(\rho_1 = 7.2 gm/cc \text{ and } \rho_2 = 8.9 gm/cc\)

\(\text{As } m_1 = m_2 \text{ and } t_1 = t_2\)

\(\text{Required ratio : } \frac{I_1}{I_2} = \frac{\frac{1}{2}M_1 R^2_1}{\frac{1}{2}M_2 R^2_2} = [\frac{R_1}{R_2}]^2\)

\(\rho = \frac{m}{V} = \frac{m}{\pi R^2}\)

\(R^2 = \frac{m}{\pi \rho t}\)

\([\frac{R_1}{R_2}]^2 = \frac{\rho_2}{\rho_1}\)

Hence, \(\frac{I_1}{I_2} = \frac{\rho_2}{\rho_1} = \frac{8.9}{7.2}\)