Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 9 - Rotational Dynamics - Focus On Concepts - Page 242: 16


c) is correct.

Work Step by Step

Because there is no work due to nonconservative forces, the total mechanical energy $E_0$ at the top of the plane is the same as the total mechanical energy $E_f$ at the bottom of the plane. Therefore, $$KE_0+PE_0=KE_f+PE_f$$ At the top of the plane, $\omega_0=0$ and $v_0=0$ so $KE_0=0$. At the bottom of the plane, $h_f=0$, so $PE_f=0$. Therefore, $$KE_f=PE_0$$ As we can see, the total kinetic energy in the end depends only the initial potential energy. Because both hoops start off at the same height, they have the same $PE_0$, so their $KE_f$ will be the same, too.
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