5. Same as problem 3, except now the track surface is rough and the sphere rolls without sliding. What is the minimal value of h such that the sphere remains on the track? (A) 2.5R + 0.7r (B) 2.7R + 1.7r (C) 2.7R − 1.7r (D) 2.5R − 1.5r (E) 2.5R + 1.5r

3. A solid sphere of mass m and radius r moves along a track with a circular loop of radius R1 as shown in following picture. It is released at height h. Assuming that the track has no friction, the ball thereforeslides down without rotation. Do not ignore the finite size of the sphere, what is the minimal value of h such that the sphere remains on the track at all times? (A) 2.5R − 1.5r (B) 2R − r (C) 2.5R (D) 2R + r (E) 2R − 1.5r

5. Same as problem 3, except now the track surface is rough and the sphere rolls without sliding. What is the minimal value of h such that the sphere remains on the track?
(A) 2.5R + 0.7r
(B) 2.7R + 1.7r
(C) 2.7R − 1.7r
(D) 2.5R − 1.5r
(E) 2.5R + 1.5r

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