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A solid sphere of mass 2 kg is rolling on a frictionless horizontal floor with a speed of 10 m/s. It then moves up a frictionless inclined plane making an angle of 30° with the horizontal. The maximum vertical height reached by the sphere before coming to rest is

1. 700 cm
2. 701 cm
3. 7.1 m
4. 70 m

Correct answer: 7.1 m

Solution

A solid sphere rolling without slipping has total KE = (7/10) m v^2 (translational + rotational). Setting (7/10) m v^2 = m g h gives h = 7 v^2/(10 g) = 7*100/98 ~ 7.14 m, i.e. about 7.1 m.

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