(A) For a conservative force $F(x)$,the potential energy $V(x)$ is defined such that the work done by the force is equal to the negative change in pot

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(A) For a conservative force $F(x)$,the potential energy $V(x)$ is defined such that the work done by the force is equal to the negative change in potential energy:$W = -\Delta V$Since the work done by a force $F$ over a small displacement $dx$ is $dW = F dx$,we have:$F dx = -dV$$F = -\frac{dV}{dx}$Thus,the negative derivative of potential energy with respect to displacement gives the conservative force.

Class 11 Physics Work, Energy, Power and Collision Conservative and Non-Conservative forces and Potential Energy

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Which quantity is obtained by taking the negative derivative of potential energy with respect to displacement in the case of a conservative force?

A
Force
B
Work
C
Power
D
Momentum

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Work, Energy, Power and Collision

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Conservative and Non-Conservative forces and Potential Energy

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Which quantity is obtained by taking the negative derivative of potential energy with respect to displacement in the case of a conservative force?

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The potential energy for a conservative system is given by:
$U = ax^2 - bx$
Where $a$ and $b$ are positive constants. The law of the force governing the system is: