A billiard ball is a uniform solid sphere of radius $3.0\ \text{cm}$, at rest on a table. A cue held horizontally gives it a sharp, short blow in a vertical plane through its centre, at a height $h$ above the table, as shown in the figure. For what value of $h$ does the ball roll without slipping straight away, so that friction from the table plays no part at all?

Fig. 1: A ball of radius R = 3.0 cm rests on a table, with its centre marked by a dot. A horizontal cue from the left strikes the ball at height h above the table.