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Work Power and Energy question

2019 · Shift 2 · Q38
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Work Power and Energy question

2019 · Shift 2 · Q38

JEE AdvancedPhysicsWork Power and EnergyMultiple correct+4 / −1
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. JEE Advanced 2019 Paper 2 Offline Physics - Work Power & Energy Question 10 English 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<<dLLv0V \lt \lt {{dL} \over L}{v_0}V<<LdL​v0​, where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?
  1. A
    After each collision with the piston, the particle speed increases by 2V.
  2. B
    If the piston moved inward by dL, the particle speed increases 2vdLL2v{{dL} \over L}2vLdL​.
  3. C
    The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from L0 to 1/2 L0.
  4. D
    The rate at which the particle strikes the piston is v/L.
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