Answer
The increasing order of moment of inertia is: $I_1, I_2, I_3$
Work Step by Step
For case 1 $I_1=\Sigma m_i r_i^2$
We plug in the known values to obtain:
$I_1=(9.0)(1.0)^2=9.0Kg.m^2$
For case 2 $I_2=\Sigma m_i r_i^2$
We plug in the known values to obtain:
$I_2=(2.5)(2.0)^2=10Kg.m^2$
For case 2 $I_2=\Sigma m_i r_i^2$
We plug in the known values to obtain:
$I_2=(2.5)(2.0)^2=10Kg.m^2$
For case 3 $I_3=\Sigma m_i r_i^2$
We plug in the known values to obtain:
$I_3=(9.0)(1.0)^2+(2.5)(2.0)^2=19Kg.m^2$
Thus, the increasing order of moment of inertia is: $I_1, I_2, I_3$
