Question

A cylinder and a hoop are rolled down an inclined plane of height h. what are their velocities at the bottom

Answer 1

Here, you have to use the work energy theorem or you can even use the mechanical energy conservation as the forces that are doing work on the objects are conservative
so you should write
total work done=change kinetic energy
only one force is working on the object i.e. gravity and the total initial kinetic energy=0
assuming that the objects will do pure rolling at the bottom, you can write angular velocity=v/r
mgh=[I(angular velocity)^2]/2 + mv^2/2
here the work done is also changing the rotational kinetic energy so we also include
[I(angular velocity)^2]/2 in our equation
and at the end i've got the folloing answers
velocity of cylinder at the bottom will be \[\sqrt{4gh/3}\]
and the velocity of the hoop will be \[\sqrt{gh}\]
if you don't get any point,please let me know
and thanks a lot for asking it was a good practice for me:)