A rigid square$-$shaped frame is constructed from four rods, each of mass $m$ and length $0\mathrm{.}50$ m $.$ The rod rotates about the axis shown in the sketch and the moment of inertia about this axis is $1\mathrm{.}25kg{m}^2.$

$($a$)$ Find the mass, $m$ of each rod.

$($b$)$ Find the torque relative to the rotation axis that will cause the frame to go from rest to angular velocity in $10\mathrm{.}0ra\frac{d}{s}$ in $5\mathrm{.}00$ seconds.

$($c$)$ Find the work done by the torque.