Portion AB of the wedge shown in figure is rough and BC is smooth. A solid cylinder rolls without slipping from A to B . Find the ratio of translational kinetic energy to rotational kinetic energy, when the cylinder reaches point C .

Step-by-step solution

aligned mgh & = 1 2 mv ^2+ 1 2 mR ^2 2 ^2 mgh & = 3 4 mv ^2 aligned aligned & 2 mgh = 1 2 mv _ f ^2+ 1 2 mR ^2 2 ^2 & 2 mgh = 1 2 mv _ f ^2+ mgh - 1 2 mv ^2 aligned aligned & mgh = 1 2 mv _ f ^2- 1 2 mv ^2 & 1 2 mv _ f ^2= 5 3 mgh aligned Ratio = 1 2 mv _ f ^2 1 2 mv ^2 2 = 5 3 mgh 1 4 4 3 mgh =5