The diagram from below shows a sphere is hanging from a ceiling by a cable whose length is R as is shown in the diagram from below. A bullet whose mass is $m$ is fired and has a speed of $v$ and travels in a straight line and gets embedded in the sphere whose mass is also $m$. As a result of the collision the sphere swings and makes a circular orbit. What should be the minimum speed of the bullet such the sphere does a circular orbit?.

The alternatives given are as follows:

$\begin{array}{ll}

1.&2\sqrt{2Rg}\\

2.&2\sqrt{Rg}\\

3.&4\sqrt{Rg}\\

4.&3\sqrt{Rg}\\

5.&\sqrt{0.5Rg}\\

\end{array}$

What I thought to solve this problem was that I can relate the momentum before and after the collision and with that speed I can relate it with the conservation of the mechanical energy when the bullet is embedded in the sphere.

This would become into:

$mv= \left(m+m\right) v_f$

$v_f=\frac{1}{2}v$

This speed can be used to relate it with the conservation of mechanical energy as follows:

$E_{k1}=E_u+E_{k2}$

$\frac{2m}{2}\left(\frac{1}{2}v\right)^2=(2m)gR+\frac{2m}{2}v_{t}^2$

$v_{t}=\textrm{Tangential speed when the ball swings}$

Then:

$\frac{v^2}{4} = 2gR+v_{t}^2$

However I end up with not knowing how to get the tangential speed or relating it to the speed which should had the bullet. How can I find it?.