A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoeselastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other endis fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $$L = L_0$$ the particle speed is $$v = v_0$$. The piston is moved inward at a very low speed V such that $$V \ll \frac{dL}{L} v_0,$$ where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?