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

Step-by-step solution

For solid sphere rolling without slipping on inclined plane, acceleration a₁= g 1+ K² R² For solid sphere slipping on inclined plane without rolling, acceleration a₂=g Therefore required ratio = a ₁ a ₂ = 1 1+ K² R² = 1 1+ 2 5 = 5 7