Question

The ratio of the acceleration for a solid sphere( mass m and radius R) rolling down an incline of angle theta without slipping and slipping down the incline without rolling is..​

Answer 1

For slipping motion on an inclined plane the acceleration for a solid sphere making an angle θ  is given by = Aslipping = g sin Ф

For rolling motion of a sphere without slipping :

The acceleration of a sphere of mass m, radius r and moment of inertia I is -

Arolling = g sin Ф/ 1+l/mr²

For a uniform sphere - l/mr² = 2/5

Thus, substituting -  

Arolling/Aslipping = g sin Ф/ g sin Ф/ 1+l/mr² = g sin Ф/g sin Ф/1+2/5

= 5/7

Therefore, the answer is 5/7.