General Dynamics

The following is the top view of an assembly kept on a smooth horizontal table. A massless inextensible string of length $D$ lies with one end fixed, while the other is attached to one end of a uniform rod of length $L$ . The system is initially at rest with the rod aligned along the $x$ -axis and the string stretched to its natural length at an angle with the negative $y$ -axis $\theta$ $(\cos \theta= \frac{1}{3})$ . At a certain instant, a bullet of the same mass $m$ as the rod and negligible dimensions is fired horizontally along the positive $y$ -direction. The bullet hits the rod at its right end with velocity $v$ and gets lodged in it, the impact being nearly instantaneous. What is the tension $(T)$ in the string immediately after the impact? Assume the string doesn’t break.
If your answer comes in the form of $T =\frac{\alpha mv^{\beta}}{\gamma} \bigg( \frac{1}{\delta D}+\frac{1}{L\sqrt{\phi}}\bigg)$
Type your answer as $\alpha +\beta+\gamma+\delta+\phi$
Details and Assumptions
1) $\alpha ,\beta,\gamma,\delta,\phi$ all are positive integer.
2) $\gamma >3$ it may help you.
The problem is not original.