A solid oylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The fatio of the acceleration of the cylinder ' a _ c ' to that of sphere ' a _ s ' is

Step-by-step solution

For sphere: M.I. I _ S = 2 5 MR ^2 For cylinder: M.I. I _ C = 1 2 MR ^2 Acceleration: a = g 1+ I MR ^2 aligned & a _ c a _ s = 1+ I _ s MR ^2 1+ I _ C MR ^2 = MR ^2+ I _ s MR ^2+ I _ c = MR ^2+ 2 5 MR ^2 MR ^2+ 1 2 MR ^2 & a _ c a _ s = 7 5 2 3 = 14 15 aligned