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JEE Advanced 2019 Paper 2

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Question : 2

Total: 54

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<<‌‌

v0 where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct ?

If the piston moves inward by dL, the particle speed increases by 2v
dL
L
After each collision with the piston, the particle speed increases by 2V
The rate at which the particle strikes the piston is v/L
The particle’s kinetic energy increases by a factor of 4 when the piston is moved inward from L0 to
1
2
L0

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