The potential energy of a body is given by U | vedclass

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(B) The relationship between force $F$ and potential energy $U$ is given by $F = -\frac{dU}{dx}$.Given the potential energy function $U = A - Bx^2$.Di

Vedclass · Accepted Answer

Proportional to $x$

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(B) The relationship between force $F$ and potential energy $U$ is given by $F = -\frac{dU}{dx}$.Given the potential energy function $U = A - Bx^2$.Differentiating $U$ with respect to $x$:$\frac{dU}{dx} = \frac{d}{dx}(A - Bx^2) = 0 - 2Bx = -2Bx$.Substituting this into the force equation:$F = -(-2Bx) = 2Bx$.The magnitude of the force is $|F| = 2Bx$.Since $2B$ is a constant,the magnitude of the force is directly proportional to the displacement $x$ $(F \propto x)$.

The potential energy of a body is given by $U = A - Bx^2$ (where $x$ is the displacement). The magnitude of the force acting on the particle is:

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