Two blocks \( m_{1} \) and \( m_{2} \) are pulled on a smooth horizontal surface, and are joined...

Two blocks \( m_{1} \) and \( m_{2} \) are pulled on a smooth horizontal surface, and are joined together with a spring of stiffness \( k \) as shown in figure. Suddenly, block \( m_{2} \) receives a horizontal velocity \( v_{0} \), then the maximum extension \( x_{m} \) in the spring is
(1) \( v_{0} \sqrt{\frac{m_{1} m_{2}}{m_{1}+m_{2}}} \)
(2) \( v_{0} \sqrt{\frac{2 m_{1} m_{2}}{\left(m_{1}+m_{2}\right) k}} \)
(3) \( v_{0} \sqrt{\frac{m_{1} m_{2}}{2\left(m_{1}+m_{2}\right) k}} \)
(4) \( v_{0} \sqrt{\frac{m_{1} m_{2}}{\left(m_{1}+m_{2}\right) k}} \)