Physics - Rotation Question with Solution | TestHub

Moment of inertia of the disc about its centre of mass and perpendicular to its plane is given by:

$I_1=\frac{1}{2}m{R}^2$

Using the parallel axis theorem, the moment of inertia about an axis at a distance $d=\frac{2R}{3}$ from the centre and perpendicular to the plane is:

$I_2=I_1+m{d}^2$

$I_2=\frac{1}{2}m{R}^2+m{\left(\frac{2R}{3}\right)}^2$

$I_2=\frac{1}{2}m{R}^2+\frac{4}{9}m{R}^2$

$I_2=\left(\frac{9+8}{18}\right)m{R}^2=\frac{17}{18}m{R}^2$

The ratio of the moments of inertia is:

$\frac{I_1}{I_2}=\frac{\frac{1}{2}m{R}^2}{\frac{17}{18}m{R}^2}=\frac{9}{17}$

Answer: $\frac{9}{17}$