A block of mass $1.0\ \text{kg}$ hangs at rest from a fixed point on a light string of length $0.80\ \text{m}$. A bullet of mass $20\ \text{g}$, moving horizontally, passes straight through the block and comes out with one third of its speed, as shown in the figure. The block is hardly changed by the hole. Take $g = 10\ \text{m/s}^2$. What is the least speed of the bullet for which the block goes right round a vertical circle?

Fig. 1: A block of mass 1.0 kg hangs from a fixed support by a string 0.80 m long. A bullet of mass 20 g moves horizontally to the right with speed u towards the block, and a faded bullet on the right side of the block leaves with speed u/3.