A \(5,0-\mathrm{kg}\) hollow cylinder of radius \(0.25 \mathrm{~m}\) rotates freely about an axle that runs through its center and along its long axis. A cord is wrapped around the cylinder and is pulled straight from the cylinder with a steady tensile force of \(50 \mathrm{~N}\). As the cord unwinds, the cylinder rotates, with no slippage between cord and cylinder.

(a) Calculate the work done by the tensile force as the cylinder rotates through \(1000 \mathrm{rad}\).

(b) If the cylinder starts from rest, calculate its rotational speed after it has rotated through \(1000 \mathrm{rad}\).