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A system comprises of two small spheres with same masses 'm'. Initially the spring is undeformed. The spheres are set in motion in gravity free space at the velocities as shown in the diagram. The maximum elastic potential Energy stored in the system is.

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$\frac{{mv}^{2}_{0}}{2 \sqrt{2}}$

${mv}_{0}^{2}$

$\frac{1}{2} {mv}^{2}_{0}$

$2 {mv}^{2}_{0}$

answer is B.

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Detailed Solution

Both spheres will come at rest simultaneously because net momentum of system is zero. And when they comes to rest, their KE converts into elastic potential energy of spring.

$U = 2 [\frac{1}{2} {mv}_{0}^{2}] = {mv}^{2}_{0}$

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