A small particle of mass m moving inside a heavy, hollow and straight tube along the tube…
Physics · JEE Advanced · NTA Exams — Work, Energy and Power
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 \(V \ll \frac{d L}{L} v_{0}\), where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?
- After each collision with the piston, the particle speed increases by 2V.
- If the piston moves inward by dL, the particle speed increases by 2v
. - The particle’s kinetic energy increases by a factor of 4 when the piston is moved inward from L0 to
. - The rate at which the particle strikes the piston is v/L.
Answer
(C) The particle’s kinetic energy increases by a factor of 4 when the piston is moved inward from L 0 to .
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