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?

Options

A. After each collision with the piston, the particle speed increases by 2V
B. If the piston moves inward by dL, the particle speed increases by `2v(dL)/L`
C. The rate at which the particle strikes the piston is v/L.
D. The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from `L_(0)` to `1/2L_(0)`

Answer

A, D