Kinetic energy of 3 rolling objects

[twerkit]

Homework Statement

Part 1:

Three objects, a solid cylinder, solid sphere, and a hoop all have equal radii and mass. They all roll down the same incline. Which of the following statements is true about the kinetic energy K
of the of the objects after they have rolled down the incline and reached the bottom?

A) K-hoop > K-cylinder
B) K-hoop > K-sphere
C) K-cylinder > K-hoop
D) K-sphere > K-cylinder
E) None of the above answers are correct

Part 2:

If the radii of the three objects differed, would the above answer still hold true? What about if the masses differed?

Homework Equations

None directly provided for this problem.

The Attempt at a Solution

**the "i's" stand for initial and "f's" stand for final**

Since the system is isolated and there is no friction energy is conserved, so

PE + KE = C (constant)

Taking derivative:

ΔPE + ΔKE = 0

PEf - PEi = 0 - mgh

ΔPE = -mgh

KEf - KEi = mgh - 0

ΔKE = mgh

Since the final potential energy is 0, the final KE = mgh. The only parameters for the energy in this situation are the objects' masses and the height of the ramp, so I believe the answer to Part 1 is:
E) None are correct

And for part 2, since the only parameters for the KE are mass and height, a difference in the radii will not change the answer to Part 1, but a difference in the masses will.

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There is no answer key for this problem, so I am checking to see if my answer is correct. If not please let me know what I did wrong. Thanks!

 

[haruspex]

Sounds good to me.