A system comprises of two small spheres with the same masses `m`. Initially, the spring is non deformed. The spheres set in motion in a gravity space at the velocities as shown in the diagram.

The maximum elastic potential energy stored in the system is

Options

A. `(mv_(0)^(2))/(2sqrt(2))`
B. `mv_(0)^(2)`
C. `(1)/(2)mv_(0)^(2)`
D. `2mv_(0)^(2)`

Answer

B

Explanation

Both sphers will come at rest simuiltaneously because net momentum of system is zero And when they comes to rest their `KE` convets into clastic potential energy of spring
`U = 2 [(1)/(2) mv_(0)^(2)] = mv_(0)^(2)`