a
\(\begin{array}{l}
\,\,\,\,\,\,\,\,\,The\,situation\,is\,shown\,in\,the\,figure.\\
Let\,v'\,be\,speed\,of\,{\rm{second}}\,block\,after\\
the\,collision.\,As\,the\,collision\,is\,elastic,\\
so\,kinetic\,energy\,is\,conserved.\\
According\,to\,conservation\,of\,kinetic\\
energy,\\
\frac{1}{2}M{v^2} + 0 = \frac{1}{2}M{\left( {\frac{v}{3}} \right)^2} + \frac{1}{2}Mv{'^2}
\end{array}\)

\(\begin{array}{l}
{v^2} = \frac{{{v^2}}}{9} + {v^2}\,or\,v{'^2} = {v^2} - \frac{{{v^2}}}{9}\\
 = \frac{{9{v^2} - {v^2}}}{9} = \frac{8}{9}{v^2}\\
v' = \sqrt {\frac{8}{9}{v^2}}  = \frac{{\sqrt 8 }}{3}v = \frac{{2\sqrt 2 }}{3}v
\end{array}\)