conservative force and potential energy questions with solutions

Showing 1–10 of 47 questions

• NumericmediumWork , Power and Energyconservative force and potential energy

  The potential energy (in joules) function of a particle in a region of space is given as : U = (2$x^2$ + 3$y^3$ + 2z) Here x, y and z are in metres. Find the magnitude of x component of force (in newton) acting on the particle at point P (1m, 2m, 3m).

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• MCQmediumWork , Power and Energyconservative force and potential energy

  A particle is at the origin and experiences F=kx (k>0). If U(0)=0, which graph correctly represents U(x)?

  Options

  • Option A

    
  • Option B

    
  • Option C

    
  • Option D

    

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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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  JEE Mains 202621 January Morning Shift

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• MCQeasyWork , Power and Energyconservative force and potential energy

  When a conservative force does positive work on a body

  Options

  • Option A

    the potential energy increases

  • Option B

    the potential energy decreases

  • Option C

    total energy increases

  • Option D

    total energy decreases

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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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• MCQmediumWork , Power and Energyconservative force and potential energy

  As a particle moves along the x–axis it is acted upon by a conservative force. The potential energy is shown below as a function of the coordinate x of the particle. Rank the labelled regions according to the magnitude of the force, least to greatest.

  

  Options

  • Option A

    AB, BC, CD

  • Option B

    AB, CD, BC

  • Option C

    BC, CD, AB

  • Option D

    BC, AB, CD

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• MCQeasyWork , Power and Energyconservative force and potential energy

  A wedge of mass M fitted with a spring of stiffness 'k' is kept on a smooth horizontal surface. A rod of mass m is kept on the wedge as shown in the figure. System is in equilibrium. Assuming that all surfaces are smooth, the potential energy stored in the spring is:

  

  Options

  • Option A

    mg²tan²θ/(2k)

  • Option B

    m²g tan²θ/(2k)

  • Option C

    m²g²tan²θ/(2k)

  • Option D

    m²g²tan²θ/k

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• MCQmediumWork , Power and Energyconservative force and potential energy

  Given below are two statements :

  Statement I : An object moves from position r₁ to position r₂ under a conservative force field F. The work done by the force is W = -∫ $\vec{F}.\vec{dr}$ from r₁ to r₂.

  Statement II : Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.

  In the light of the above statements, choose the correct answer from the options given below :

  Options

  • Option A

    Both Statement I and Statement II are true

  • Option B

    Statement I is false but Statement II is true

  • Option C

    Statement I is true but Statement II is false

  • Option D

    Both Statement I and Statement II are false

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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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  JEE Mains 2025 28 Jan Morning Shift

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

  For a one-dimensional conservative system, which statements are correct?

  Select all that apply

  • Option A

    F = -dU/dx

  • Option B

    Stable equilibrium occurs at a local minimum of U

  • Option C

    Unstable equilibrium occurs at a local maximum of U

  • Option D

    At every point where U = 0, force must be zero

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