બે m દળના બ્લોક A અને B ને L લંબાઇ અને k બ

Initial momentum of the system (block $C$) $= mv$
After striking with $A$, the block $C$ comes to rest and now both block $A$ and $B$ moves with velocity $V$, when compression in spring is maximum.
By the law of conservation of linear momentum
$mv = (m + m) V$ ==> $V = \frac{v}{2}$
By the law of conservation of energy
$K.E.$ of block $C = K.E. $ of system $+ P.E.$  of system
$\frac{1}{2}m{v^2} = \frac{1}{2}(2m)\,{V^2} + \frac{1}{2}k{x^2}$
==> $\frac{1}{2}m{v^2} = \frac{1}{2}(2m)\;{\left( {\frac{v}{2}} \right)^2} + \frac{1}{2}k{x^2}$
==> $k{x^2} = \frac{1}{2}m{v^2}$
==> $x = v\sqrt {\frac{m}{{2k}}} $