Two identical blocks \( A \) and \( B \), each of mass ' \( m \) ' resting on smooth floor are c...

Two identical blocks \( A \) and \( B \), each of mass ' \( m \) ' resting on smooth floor are connected by a light spring of natural length \( L \) and spring constant \( \mathrm{K} \), with the spring at its natural length. A third identical block ' \( C \) ' (mass m) moving with a speed \( v \) along the line joining \( A \) and \( B \) collides with \( A \). The maximum compression in the spring is
[EAMCET 2003]
(a) \( v \sqrt{\frac{m}{2 k}} \)
(b) \( m \sqrt{\frac{v}{2 k}} \)
(c) \( \sqrt{\frac{m v}{k}} \)
(d) \( \frac{m v}{2 k} \)