Conservative Forces & Potential Energy questions with solutions

Showing 1–10 of 47 questions

• MCQmediumWork , Power and EnergyConservative Forces & 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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• Multi-correctmediumWork , Power and EnergyConservative Forces & Potential Energy

  Which of the following forces are conservative?

  Select all that apply

  • Option A

    $\vec{F}$=2r³r̂

  • Option B

    $\vec{F}$=-(5/r)r̂

  • Option C

    $\vec{F}$=3(xî+yĵ)/(x²+y²)^(3/2)

  • Option D

    $\vec{F}$=3(yî+xĵ)/(x²+y²)^(3/2)

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• Multi-correctmediumWork , Power and EnergyConservative Forces & 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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• MCQeasyWork , Power and EnergyConservative Forces & 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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• NumericmediumWork , Power and EnergyConservative Forces & 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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• NumericeasyWork , Power and EnergyConservative Forces & 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 Forces & 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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• NumericmediumWork , Power and EnergyConservative Forces & 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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• NumericmediumWork , Power and EnergyConservative Forces & Potential Energy

  The potential energy of a 2 kg particle moving along the x-axis is U(x)=(4.0 J/m²)x²+(1.0 J/m⁴)x⁴. When the particle is at x=1.0 m, find the magnitude of its acceleration in m/s². Only conservative forces act.

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• MCQeasyWork , Power and EnergyConservative Forces & Potential Energy

  Which force cannot be expressed in terms of a potential-energy function?

  Options

  • Option A

    Coulomb force

  • Option B

    Gravitational force

  • Option C

    Frictional force

  • Option D

    Restoring force

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