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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   where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?
  • a)
    The rate at which the particle strikes the piston is v/L
  • b)
    After each collision with the piston, the particle speed increases by 2V
  • c)
    The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from 
  • d)
    If the piston moves inward by dL, the particle speed increases by 
Correct answer is option 'B,C'. Can you explain this answer?
Verified Answer
A small particle of mass m moving inside a heavy, hollow and straight ...

(1) average rate of collision = 2L/v.
(2) speed of particle after collision = 2V + v0
change in speed = (2V + v0) – v0
after each collision = 2V
no. of collision per unit time (frequency) = v/2L
change in speed in dt time = 2V × number of collision in dt time



or


vx = constant  ⇒ on decreasing length to half K.E. becomes 1/4
vdx + xdv = 0
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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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer?
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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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer?.
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Here you can find the meaning of 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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of 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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer?, a detailed solution for 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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer? has been provided alongside types of 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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice 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 verylow speed V such that where dL is the infinitesimal displacement of the piston. Whichof the following statement(s) is/are correct?a)The rate at which the particle strikes the piston is v/Lb)After each collision with the piston, the particle speed increases by 2Vc)The particles kinetic energy increases by a factor of 4 when the piston is moved inward fromd)If the piston moves inward by dL, the particle speed increases byCorrect answer is option 'B,C'. Can you explain this answer? tests, examples and also practice JEE tests.
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