A particle of mass m moving with velocity V₀ strikes a simple pendulum of mass m and sticks to it. The maximum height attained by the pendulum will be 

Initial momentum of particle = mV₀
Final momentum of system (particle + pendulum) = 2mv
By the law of conservation of momentum 
$\Rightarrow {\mathrm{mV}}_0=2\mathrm{mv}\Rightarrow$Initial velocity of system $\mathrm{v}=\frac{{\mathrm{V}}_0}{2}$
$\therefore$ Initial K.E. of the system = $\frac{1}{2}\left(2\mathrm{m}\right){\mathrm{v}}^2=\frac{1}{2}\left(2\mathrm{m}\right){\left(\frac{{\mathrm{V}}_0}{2}\right)}^2$
If the system rises up to height h then P.E. =  2mgh
By the law of conservation of energy 
$\frac{1}{2}\left(2\mathrm{m}\right){\left(\frac{{\mathrm{V}}_0}{2}\right)}^2=2\mathrm{mgh}\Rightarrow \mathrm{h}=\frac{{\mathrm{V}}_0^2}{8\mathrm{g}}$