Question

A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and horizontally by a cue. Where should it be hit so that the shell does not slip on the surface?

Answer 1

The shell should hit at height h = 2R / 3

Explanation:

Let the cue strikes at as height h above the center for pure rolling

Vc = Rω

Applying law of conservation of angular momentum at point A.

Linear momentum imported to sphere = x

Vc = rωc

−μCh−θω=0

mvCh = 2 / 3 m R^2(Vo / R)

mvCh = 2 / 3mR^2(Vo / R)

h = 2R / 3

Thus the shell should hit at height h = 2R / 3

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