The potential energy of a body is given by U=A-Bx^2 (where x is displacement). The magnitude of

Step 1:u000AThe potential energy of the body is given by $u005Cmathrm{U}u003Du005Cmathrm{A}u002Du005Cmathrm{Bx}^{2}$, wh

The potential energy of a body is given by U=A-Bx^2 (where x...

The potential energy of a body is given by $\mathrm{U}=\mathrm{A}-\mathrm{Bx}^{2}$ (where $\mathrm{x}$ is displacement). The magnitude of force acting on the particle is (A) constant (B) proportional to $\mathrm{x}$ (C) proportional to $\mathrm{x}^{2}$ (D) Inversely proportional to $\mathrm{x}$

The potential energy of a body is given by $\mathrm{U}=\mathrm{A}-\mathrm{Bx}^{2}$ (where $\mathrm{x}$ is displacement). The magnitude of force acting on the particle is
(A) constant
(B) proportional to $\mathrm{x}$
(C) proportional to $\mathrm{x}^{2}$
(D) Inversely proportional to $\mathrm{x}$

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Key Concepts

Potential Energy Function

A potential energy function represents the energy stored in a system due to its position or configuration. It provides a way to analyze forces through the spatial variation of energy. By examining how potential energy changes with displacement, one can determine the force acting on the system.

Differentiation in Mechanics

Differentiation is a mathematical tool used to compute the rate of change of a function. In the context of classical mechanics, taking the derivative of the potential energy function with respect to displacement yields the force acting on a particle. This method is crucial for translating energy functions into force laws.

Conservative Forces

Conservative forces are forces that can be described as the negative gradient of a potential energy function. In these systems, the work done by the force is independent of the path taken, and energy is conserved. This concept is fundamental in understanding how forces derive from energy functions in mechanics.

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