A thin, very light wire is wrapped around a drum that is free to rotate. The free end of the wire is attached to a ball of mass m$.$ The drum has the same mass m$.$ Its radius is R and its moment of inertia is I $=(1/2)$mR$2.$ As the ball falls, the drum spins.

At an instant that the ball has translational kinetic energy K$,$ what is the rotational kinetic energy of the drum?

Group of answer choices

$2$K

K$/2$

K

K$/4$