A narrow glass tube, with the same cross-section everywhere, is bent into a V whose arms slope at $30^\circ$ and at $45^\circ$ to the horizontal (see the figure). Liquid fills $0.60\ \text{m}$ of its length, along its axis. The liquid is displaced slightly and released, and it rocks to and fro. Neglect viscosity and the short bend at the bottom, with $g = 10\ \text{m/s}^2$. Find the period.

Fig. 1: A thin tube bent into a V, with its lowest point at the bottom. The left arm rises at 30 degrees to the horizontal and the right arm at 45 degrees. Liquid fills the bottom of the V and part of each arm, and its two surfaces are at the same height when it is at rest. A label says the liquid column is 0.60 m long, measured along the tube.