A solid sphere rolls without slipping on an inclined plane at an angle . The ratio of total kinetic energy to its rotational kinetic energy is

Step-by-step solution

Moment of Inertia of a solid sphere, I= 2 5 MR ^2 Since there is no slipping, v = R Rotational kinetic energy E _ Tot = 1 2 I ^2 aligned & = 1 2 2 5 M R ^2 ^2 & = MR ^2 ^2 5 & = MV ^2 5 ... (i) aligned Total kinetic energy aligned E _ K & = 1 2 I ^2+ 1 2 MV ^2 & = MV ^2 5 + MV ^2 2 & = 7 MV ^2 10 ... (ii) aligned Dividing (ii) by (i), we get, E _ K E _ me = ( 7 MV ^2 10 ) ( MV ^2 5 ) = 7 2