$1247893$

$17.$ Two blocks A and $B$ of mass $m$ and $2m$ respectively, are connected by a spring of stiffness $K$ and placed on a smooth horizontal surface. Initially the spring has its equilibrium length. Blocks A and $B$ are given velocity vo and $2v_0$ as shown. The maximum extension in the spring is

$(1)\sqrt[\phantom{2}]{\frac{m}{k}}{v}_0$

$(2)\sqrt[\phantom{2}]{\frac{m}{2K}}{v}_0$

$(3)\sqrt[\phantom{2}]{\frac{2m}{3K}}{v}_0$

$(4)\sqrt[\phantom{2}]{\frac{4m}{3K}}{v}_0$