A body of mass m slides down an incline and reaches the bottom with a velocity V . If the same mass were in the form of a disc which rolls down this incline, the velocity of the disc at bottom would have been

Step-by-step solution

Case 1: 1 2 m V^2=m g h Case 2: 1 2 ~m ( v ^ )^2+ 1 2 I ^2= mgh For disc, I = 1 2 mR ^2 aligned & 1 2 m (v^ )^2+ 1 2 ( 1 2 m R^2 ) (v^ )^2 R^2 =m g h & 1 2 m (v^ )^2+ 1 4 m (v^ )^2=m g h & 3 4 m (v^ )^2=m g h ....(ii) aligned From (i) and (ii), aligned & 1 2 m V^2= 3 4 m v^ 2 & v^ = 2 3 V aligned