A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is x 5 where x = _____

Step-by-step solution

Applying Mechanical Energy conservation : k _ i + U _ i = k _ f + U _ f aligned & 0+ Mgh = 1 2 mv ^2 (1+ k ^2 R ^2 )+0 & ~V = 2 gh 1+ k ^2 R ^2 aligned So Ratio of velocities V _ Ring V _ solids sphere = 1+ 2 5 1+1 = 7 10 x =3.5 Rounding off x =4