Question

A system comprises of two small spheres with same masses ${}^{\prime }{m}^{\prime }$. Initially the spring is non-deformed. 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
Diagram

• A. $2m{v}_0^2$
• B. $\frac{1}{2}m{v}_0^2$
• C. $m{v}_0^2$
• D. $\frac{m{v}_0^2}{2\sqrt{2}}$

Answer 1

The correct option is C $m{v}_0^2$

As per the given diagram,
Both spheres will come at rest simultaneously because net momentum of system is zero. And when they come to rest, their $K.E$ converts into elastic potential energy of spring.
Therefore,
$U=2\left[\frac{1}{2}m{v}_0^2\right]$
$U=m{v}_0^2$

Final Answer: (b)