KVPY SX SB Exam 2015 Question Paper

Initially wire is slack so it do not have any deformation energy. When block is given some velocity it move due to kinetic energy, one wire get taut. Internal force get develop in wire and KE start decreases and deformation energy of wire increase. Till block come at rest using energy conservation
$\frac{1}{2}\mathit{m}{\mathit{v}}^2=\frac{1}{2}\mathit{Y}\times {\left(\mathrm{strain}\right)}^2\times \mathit{A}\times \mathit{L}$
$\frac{1}{2}\mathit{m}{\mathit{v}}^2=\frac{1}{2}\mathit{Y}\times {\left(\frac{\mathit{x}}{\mathit{L}}\right)}^2\times \mathit{A}\times \mathit{L}$
$\mathit{x}=\mathit{v}\sqrt{\frac{\mathit{m}\mathit{L}}{\mathit{A}\mathit{Y}}}$