A disc shaped body has two tight windings of light threads - one on the inner rim of radius `R = 1m` and the other on outer rim of radius `2R` (see figure). It is kept on a horizontal surface and the ends of the two threads are pulled horizontally in opposite directions with force of equal magnitude `F = 20N`. Mass of the body and its moment of inertia about an axis through centre O and perpendicular to the plane of the figure are `M = 4kg` and `I = 8 kg - m^(2)` respectively. Find the kinetic energy of the body 2 seconds after the forces begin to act, if
(i) the surface is smooth,
(ii) the surface is rough enough to ensure rolling without sliding.

Answer

(i) 100 J
(ii) 33.33 J