Question

A system comprises of two small spheres with the same masses $m$. Initially, the spring is non-deformed. The spheres are set in motion in a gravity-free space at the velocities as shown in the diagram.
The maximum elastic potential energy stored in the system is

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

Answer 1

The correct option is B ${mv}_0^2$

Both the sphere 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.

Maximum elastic potential energy$=$ Kinetic energy of the system.

$=\frac{1}{2}m{v}_0^2+\frac{1}{2}m{v}_0^2=m{v}_0^2$