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A particle free to move along the x-axis has potential energy given by U(x) = k [1–exp(–x2)] for -∞ < x < + ∞, where k is a positive constant of appropriate dimensions. Then
  • a)
    at points away from the origin, the particle is in unstable equilibrium
  • b)
    for any finite nonzero value of x, there is a force directed away from the origin
  • c)
    if its total mechanical energy is k/2, it has its minimum kinetic energy at the origin.
  • d)
    for small displacements from x = 0, the motion is simple harmonic
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A particle free to move along the x-axis has potential energy given by...
Let us plot the graph of the mathematical equation
From the graph it is clear that the potential energy is minimum at x =  0. Therefore, x = 0 is the state of stable equilibrium. Now if we displace the particle from x = 0 then for displacements the particle tends to regain the position x = 0 with a force  Therefore for small
values of x we have F ∝ x.
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A particle free to move along the x-axis has potential energy given by U(x) = k [1–exp(–x2)] for -∞ < x < + ∞, where k is a positive constant of appropriate dimensions. Thena)at points away from the origin, the particle is in unstable equilibriumb)for any finite nonzero value of x, there is a force directed away from the originc)if its total mechanical energy is k/2, it has its minimum kinetic energy at the origin.d)for small displacements from x = 0, the motion is simple harmonicCorrect answer is option 'D'. Can you explain this answer?
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A particle free to move along the x-axis has potential energy given by U(x) = k [1–exp(–x2)] for -∞ < x < + ∞, where k is a positive constant of appropriate dimensions. Thena)at points away from the origin, the particle is in unstable equilibriumb)for any finite nonzero value of x, there is a force directed away from the originc)if its total mechanical energy is k/2, it has its minimum kinetic energy at the origin.d)for small displacements from x = 0, the motion is simple harmonicCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle free to move along the x-axis has potential energy given by U(x) = k [1–exp(–x2)] for -∞ < x < + ∞, where k is a positive constant of appropriate dimensions. Thena)at points away from the origin, the particle is in unstable equilibriumb)for any finite nonzero value of x, there is a force directed away from the originc)if its total mechanical energy is k/2, it has its minimum kinetic energy at the origin.d)for small displacements from x = 0, the motion is simple harmonicCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle free to move along the x-axis has potential energy given by U(x) = k [1–exp(–x2)] for -∞ < x < + ∞, where k is a positive constant of appropriate dimensions. Thena)at points away from the origin, the particle is in unstable equilibriumb)for any finite nonzero value of x, there is a force directed away from the originc)if its total mechanical energy is k/2, it has its minimum kinetic energy at the origin.d)for small displacements from x = 0, the motion is simple harmonicCorrect answer is option 'D'. Can you explain this answer?.
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