A light inextensible string lies with one end fixed, while the other is attached to one  end of a uniform rod of length  $l$  and mass m. The system is initially at rest with the rod  aligned along the x-axis and the string at an angle with the negative y-axis  $\theta$ .  $(\cos \theta =\frac{1}{3})$
A bullet of mass m (same as that of the rod  is fired which hits the rod at its right end with  velocity  ${\text{v}}_{\text{o}}$ and gets lodged in it. Assume the string doesn’t break. The end of the  string  tied to the rod is point P.

(top view of an assembly kept on a smooth horizontal table)
Which of the following statements are correct?