Tow blocks $m_1$ and $m_2$ are placed on a smooth horizontal surface and are joined together with a spring of stiffness k. Suddenly, block $m_2$ receives a horizontal velocity $v_0$, then the maximum extension $x$ in the spring is

Question

$$\begin {array} {1 1} (a)\;v_o \sqrt {\frac{m_1m_2}{v(m_1+m_2)}} & \quad (b)\;v_o \sqrt {\frac{2m_1m_2}{(m_1+m_2)R}} \\ (c)\;v_o \sqrt {\frac{m_1m_2}{2(m_1+m_2)k}} & \quad  (d)\;v_o \sqrt {\frac{m_1m_2}{(m_1+m_2)k}} \end {array}$$