A solid sphere, a solid cylinder, a spherical shell, and a hoop all have the sam

Question

A solid sphere, a solid cylinder, a spherical shell, and a hoop all have the same mass and radius. Each are rolling on a horizontal surface with the same center of mass speed, and then they roll up identical inclines. Which one goes the greates distance up its incline?

a. the hoop
b. the solid sphere
c. the spherical shell
d. the cylinder
e. they all go the same distance up their inclines.

Explanation / Answer

Total kinetic energy K = ( 1/ 2) mv^ 2 * [ 1+ ( k/r)^ 2] (k/ r)^ 2 of solid sphere = ( 2/ 5) of solid cylinder = ( 1/ 2) of spherical shell = ( 2/ 3) of hoop = 1 So, K"' > K" >K ' > K from law of conservation of energy , potential energy at top of the incline of hoop is large. So, answer is the hoop

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