A uniform disc of mass m is fitted (pivoted smoothly) with a rod of mass m2. If the bottom of the rod is pulled with a velocity v, it moves without changing its angle of orientation and the disc rolls without sliding. Thd kinetic energy of the system (rod + disc) is.

Rolling can be considered as pure rotation about point of contactKrolling = 12IPω2 = 12(mR22+mR2)ω2 = 34mR2ω2-----------(i)The rod translates with the velocity v hence velocity of centre of disc will also be vv = ωR------(ii)From (i) and (ii); Krolling = 34mv2Kinetic energy of the rod Krod = 12(m2)v2 = mv24-------(iii)Ktotal = Krolling+Krod = mv2