The Inclined Plane Race: Sphere vs. Hoop

[Tricks67]

a sphere and a hoop both of same mass (e.g. 'm') roll down an inclined plane without slipping...which will get to the bottom first..will they have equal kinetic energies when they reach the bottom?

 

[rcgldr]

This appears to be homework. If so, you're supposed to show some attempt at solving the problem.

 

[Tricks67]

nope not hw..(i wish our homework wud have had such long deadlines)...some problems given in a book...and i post the ones, i can't approach..

 

[Malor]

nope not hw..(i wish our homework wud have had such long deadlines)...some problems given in a book...and i post the ones, i can't approach..

No... though both objects have the same potential Energy at t = 0s, they have different "moments of inertia" and since they are both rolling they have both kinetic and rotational Energy when they reach the bottom of the inclined plane. The hoop will be slower.

E_rot = 1/2 J ω²