The bob of pendulum at rest is given a sharp hit to impart a horizontal velocity $\sqrt{6gl},$ where l is
the length of the pendulum. Find the tension when string becomes vertical. (g = acceleration due
to gravity)

 The bob will make complete revolution and at the highest point of its trajectory ,using conservation of mechanical energy 

$$\begin{gathered} \frac{1}{2}m{v}^2+mg . 2l = \frac{1}{2}m {\left(\sqrt{6gl}\right)}^2 \\ (v=\text{ speed at highest point) } \\ \Rightarrow v =\sqrt{2gl} \end{gathered}$$

$\mathrm{T}=\frac{{\mathrm{mv}}^2}{\mathrm{l}}-\mathrm{mg}=2\mathrm{mg}-\mathrm{mg}=\mathrm{mg}$