Answer
$\alpha_C \lt \alpha_B \lt \alpha_A$
Work Step by Step
We can rank the given three cases in order of increasing acceleration as follows:
For case A:
$I_A=m_1r_1^2+m_2r_2^2+m_3r_3^2$
$\implies I_A=(9.0)(1.0)^2+0+0=9.0Kg.m^2$
For case B:
$I_B=0+0+(2.5)(2.0)^2$
$I_B=10Kg.m^2$
For case C:
$I_C=(9.0)(1.0)^2+0+(2.5)(2.0)^2$
$I_C=19Kg.m^2$
Since angular acceleration is inversely proportional to the angular momentum $I$, we can rank the given cases in increasing order of angular acceleration as
$\alpha_C \lt \alpha_B \lt \alpha_A$
