As per the given figure, two blocks each of mass 250g are connected...

Let the maximum elongation of the spring be $x$.

Using energy conservation

Loss in kinetic energy of both blocks=Gain in spring energy

$\dfrac{1}{2}m{v}^{2} \times 2 = \dfrac{1}{2}k{x}^{2}$

$⇒ \left(0 . 25\right){v}^{2} = \dfrac{1}{2} \times 2 \times {x}^{2}$

$⇒ \dfrac{1}{4}{v}^{2} = \dfrac{1}{2} \times 2 \times {x}^{2}$

$∴ x = \dfrac{v}{2}$