Question

Two circular discs have masses in the ratio 1:2 and diameters in the ratio 2:1. The ratio of their moments of inertia about similar axes is

Answer 1

HEY here is your answer

Answer 2

The ratio of the moment of inertia of both the circular disks about the similar axis is 2:1 .

• Given :

Ratio of masses of the disks (m₁:m₂)= 1:2

Ratio of diameters of the disks (d₁:d₂)= 2:1

Now, the moment of inertia about a central axis is given by

I = $\frac{1}{2}mr^2$

• Now, ratio of moment of inertia of the circular disks will be ,

$\frac{I_1}{I_2}$ = $\frac{\frac{1}{2}m_1(r_1)^2}{\frac{1}{2}m_2(r_2)^2}$

• Ratio of moment of inertia of the disks with diameter,

$\frac{I_1}{I_2}$ = $\frac{\frac{1}{2}m_1(d_1/2)^2}{\frac{1}{2}m_2(d_2/2)^2}$

$\frac{I_1}{I_2}$ = $\frac{m_1(d_1/2)^2}{m_2(d_2/2)^2}$

• Substituting the known ratios, we get

$\frac{I_1}{I_2}$ = $(\frac{1}{2})(\frac{4}{1})$

$\frac{I_1}{I_2}$ = 2

• Ratio of inertia of the circular disks = 2:1