A solid cylinder of mass M and radius R rolls without slipping on an inclined plane of length L and height h . What is the speed of its centre of mass when the cylinder reaches its bottom?

Step-by-step solution

Here K.E. of centre of mass when cylinder reached the bottom = 1 2 m v^2+ 1 2 I ^2 ( i ) Here I = 1 2 M K^2 and = V R aligned & KE = 1 2 m v^2+ 1 2 M K^2 V^2 r^2 & = 1 2 m v^2 [1+ K^2 R^2 ] aligned But for solid cylinder K= R 2 or K^2 R^2 = 1 2 K E= 3 4 m v^2 PE of the solid cylinder at height h is PE =m g h From eq. (ii) and (iii) aligned & m g h= 3 4 m v^2 & v= 4 3 g h aligned