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A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collision
  • a)
    The speed of the particle when it returns to its equilibrium position is u0
  • b)
    The time at which the particle passes through the equilibrium position for the first time is 
  • c)
    The time at which the maximum compression of the spring occurs is 
  • d)
    The time at which the particle passes through the equilibrium position for the second time is 
Correct answer is option 'A,D'. Can you explain this answer?
Verified Answer
A particle of mass m is attached to one end of a mass-less spring of f...
The particle collides elastically with rigid wall. Here 

i.e. the particle rebounds with the same speed. Therefore the particle will return to its equilibrium position with speed u0. option (a) is correct.
The velocity of the particle becomes 0.5u0 after time t.
Then using the equation V = Vmax cos wt we get 0.5u0 = u0 cos wt

The time period 
The time taken by the particle to pass through the equilibrium for the first time   Therefore option (b) is incorrect
The time taken for the maximum compression
  Therefore option c is incorrect.
The time taken for particle to pass through the equilibrium position second time
option (d) is correct.
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A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collisiona)The speed of the particle when it returns to its equilibrium position is u0b)The time at which the particle passes through theequilibrium position for the first time is c)The time at which the maximum compression of the spring occurs is d)The time at which the particle passes through the equilibrium position for the second time is Correct answer is option 'A,D'. Can you explain this answer?
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A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collisiona)The speed of the particle when it returns to its equilibrium position is u0b)The time at which the particle passes through theequilibrium position for the first time is c)The time at which the maximum compression of the spring occurs is d)The time at which the particle passes through the equilibrium position for the second time is Correct answer is option 'A,D'. 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 particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collisiona)The speed of the particle when it returns to its equilibrium position is u0b)The time at which the particle passes through theequilibrium position for the first time is c)The time at which the maximum compression of the spring occurs is d)The time at which the particle passes through the equilibrium position for the second time is Correct answer is option 'A,D'. 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 particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collisiona)The speed of the particle when it returns to its equilibrium position is u0b)The time at which the particle passes through theequilibrium position for the first time is c)The time at which the maximum compression of the spring occurs is d)The time at which the particle passes through the equilibrium position for the second time is Correct answer is option 'A,D'. Can you explain this answer?.
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