The ratio of the accelerations for a solid sphere (mass m and radius R ) rolling down an incline of angle  θ  without slipping and slipping down the incline without rolling is

Acceleration of the solid sphere slipping down the incline without rolling isaslipping =gsin⁡θAcceleration of the solid sphere rolling down the incline without slipping is arolling =gsin⁡θ1+k2R2=gsin⁡θ1+25∵ For solid sphere, k2R2=25=57gsin⁡θ                         .....(ii)Divide eqn. (ii) by eqn. (i), we getarolling aslipping =57