A certain merry$-$go$-$round is accelerated uniformly from rest and attains an angular speed of $0\mathrm{.}4$ rad$/$s in the first $10$ seconds. If the net applied torque is $2000$ N $$ m$,$ what is the moment of inertia of the merry$-$go$-$round?

A$.$

$800$ kg$.$ m$2$

B$.$

$5000$ kg$.$ m$2$

C$.$

$50,000$ kg$.$ m$2$

D$.$

This cannot be determined since the radius is not specified.