A small projectile of mass \(m\) is moving horizontally with speed \(v_0\) when it strikes the bottom end of a uniform thin rod of mass \(M\) and length \(L\). The rod is pivoted at its top end and is initially at rest, hanging vertically. The projectile becomes embedded in the rod during the collision, and the rod-projectile system then swings upward until the rod makes a maximum angle \(\theta\) with the vertical. Which of the following expressions is correct for \(\cos\theta\)?