A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is 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 < < (dL)/(L) v_0`, where dL is the infinitesimal displacement of the piston. Which of the following statements(s) is(are) correct?