Question

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 = L₀ the particle speed is v = v₀.

The piston is moved inward at a very low speed V such that v<<dL/L v₀ , where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?

(A) If the piston moves inward by dL, the particle speed increases by 2v  dL/L

(B) The particle’s kinetic energy increases by a factor of 4 when the piston is moved inward from L₀ to 1/2 L₀

(C) After each collision with the piston, the particle speed increases by 2V

(D) The rate at which the particle strikes the piston  v/L

Answer 1

Correct option (B,C)

Explanation:

Initial velocity of particle is v = v₀ 

And distance of piston x = L₀

dx is (–ve)

Vdt = –dx(distance moved by piston)

∴ KE increases by 4 times.