conservative force and potential energy questions with solutions

Showing 1–10 of 15 questions

• NumericeasyWork , Power and Energyconservative force and potential energy

  Potential energy of a particle changes from 35 J to -15 J. If work done by the conservative force is N joule, find N.

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• MCQmediumWork , Power and Energyconservative force and potential energy

  The potential energy of a particle is U(x) = ax⁴ - bx², where a>0 and b>0. Which statement is correct?

  Options

  • Option A

    x = 0 is a stable equilibrium

  • Option B

    x = 0 is an unstable equilibrium

  • Option C

    No other equilibrium positions exist

  • Option D

    All equilibrium positions are unstable

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• MCQmediumWork , Power and Energyconservative force and potential energy

  A force field in the xy-plane has components Fₓ = 2xy + 3 and Fᵧ = x² + 4y. Which potential energy function is possible?

  Options

  • Option A

    U = -x²y - 3x - 2y² + C

  • Option B

    U = x²y + 3x + 2y² + C

  • Option C

    U = -2xy - 4y + C

  • Option D

    The force is non-conservative

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• MCQmediumWork , Power and Energyconservative force and potential energy

  Potential energy (V) versus distance (x) is given by the graph, Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.

  

  Options

  • Option A

    F₍ʙᴄ₎ > F₍ᴄᴅ₎ > F₍ᴅᴇ₎ > F₍ᴀʙ₎

  • Option B

    F₍ᴄᴅ₎ > F₍ᴀʙ₎ > F₍ʙᴄ₎ > F₍ᴅᴇ₎

  • Option C

    F₍ᴄᴅ₎ > F₍ᴅᴇ₎ > F₍ᴀʙ₎ > F₍ʙᴄ₎

  • Option D

    F₍ʙᴄ₎ > F₍ᴀʙ₎ > F₍ᴅᴇ₎ > F₍ᴄᴅ₎

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• NumericeasyWork , Power and Energyconservative force and potential energy

  A particle moves in the one-dimensional potential U(x) = x² + 4x + 10 J with total mechanical energy 15 J. If the turning points are x₁ and x₂, find |x₁ - x₂|.

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• NumericmediumWork , Power and Energyconservative force and potential energy

  A particle experiences the one-dimensional force F(x) = 6x - 4x³ N. If U(0) = 0 and U(1) = N joule, find N.

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• MCQmediumWork , Power and Energyconservative force and potential energy

  Assertion: Work done by a central force is independent of path. Reason: Potential energy is associated with every force.

  Options

  • Option A

    Both Assertion and Reason are correct

  • Option B

    Assertion is correct, Reason is incorrect

  • Option C

    Assertion is incorrect, Reason is correct

  • Option D

    Both Assertion and Reason are incorrect

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• Multi-correctmediumWork , Power and Energyconservative force and potential energy

  At a point x = x₀ in a one-dimensional potential, dU/dx = 0. Which statements may be true?

  Select all that apply

  • Option A

    The particle is at an equilibrium position

  • Option B

    Force is zero at that point

  • Option C

    The equilibrium may be stable

  • Option D

    The equilibrium may be unstable

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• A/ReasyWork , Power and Energyconservative force and potential energy

  Evaluate the following statements.

  Assertion

  Assertion (A): Work done by a conservative force over a closed path is zero.

  Reason

  Reason (R): Work done by a conservative force between two points depends only on the initial and final positions.

  Options

  • Option A

    Both A and R are true and R is the correct explanation of A.

  • Option B

    Both A and R are true but R is NOT the correct explanation of A.

  • Option C

    A is true but R is false.

  • Option D

    A is false but R is true.

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• Multi-correctmediumWork , Power and Energyconservative force and potential energy

  For a particle moving in a one-dimensional conservative potential U(x) with total energy E, which statements are correct?

  Select all that apply

  • Option A

    Motion is allowed where E ≥ U(x)

  • Option B

    At a turning point E = U(x)

  • Option C

    At every turning point acceleration is zero

  • Option D

    Kinetic energy is E - U(x)

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