A uniform marble rolls without slipping down the path shown in Fig. P10.80, starting from rest. 

(a) Find the minimum height h required for the marble not to fall into the pit.

(b) The moment of inertia of the marble depends on its radius. Explain why the answer to part (a) does not depend on the radius of the marble.

(c) Solve part (a) for a block that slides without friction instead of the rolling marble. How does the minimum h in this case compare to the answer in part (a)?

Figure P10.80:

45 m Pit 25 m 36 m