a
\(\begin{array}{l}
\,\,\,\,\,\,\,Here,\,{m_{1\,}} = m,{m_2} = 2m\\
\,\,\,\,\,\,{u_1} = 2m/s,\,{u_2} = 0\\
Coefficient\,of\,restitution,\,e = 0.5\\
Let\,{v_1}\,and\,{v_2}\,be\,their\,respective\,\\
velocities\,after\,collision.\\
Applying\,the\,law\,of\,conservation\,of\\
linear\,momentum,\,we\,get\\
\,\,\,\,\,\,\,\,\,\,\,\,\,{m_1}{u_1} + {m_2}{u_2} = {m_1}{v_1} + {m_2}{v_2}\\
\,\,\,\,\,\,\,\,\,\,\,\,\,m \times 2 + 2m \times 0 = m \times {v_1} + 2m \times {v_2}
\end{array}\)

\(\begin{array}{l}
or\,\,2m = m{v_1} + 2m{v_2}\,or\,2 = \left( {{v_1} + 2{v_2}} \right)\,\,\,\,...\left( i \right)\\
By\,definition\,of\,coefficient\,of\,restitution,\\
\,\,\,\,\,\,\,\,\,\,\,\,e = \frac{{{v_2} - {v_1}}}{{{u_1} - {u_2}}}\\
or\,\,\,\,\,\,\,e\left( {{u_1} - {u_2}} \right) = {v_2} - {v_1} \Rightarrow 0.5\,\left( {2 - 0} \right)\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {v_2} - {v_1}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)\\
Solving\,equations\,\left( i \right)\,and\,\left( {ii} \right),\,we\,get\\
\,\,\,\,{v_1} = 0\,m/s,\,{v_2} = 1\,m/s
\end{array}\)