Answer
$2.6~J~~$ of work is required.
Work Step by Step
We can find the rotational inertia:
$I = 2Ma^2+2Ma^2+M(\sqrt{b^2-a^2})^2$
$I = 4Ma^2+M(b^2-a^2)$
$I = (4)(0.40~kg)(0.30~m)^2+(0.40~kg)[(0.50~m)^2-(0.30~m)^2]$
$I = 0.208~kg~m^2$
We can find the rotational kinetic energy:
$K = \frac{1}{2}I~\omega^2$
$K = (\frac{1}{2})(0.208~kg~m^2)~(5.0~rad/s)^2$
$K = 2.6~J$
$2.6~J~~$ of work is required.
