Question

For one dimensional motion, the force F(x) and the potential energy U(x) are related as:
1. \(F(x)=\dfrac{-dU(x)}{dx}\)
2. \(F(x)=\dfrac{dU(x)}{dx}\)
3. \(U(x)=\dfrac{dF(x)}{dx}\)
4. \(U(x)=\dfrac{-dF(x)}{dx}\)

Answer 1

Correct Answer - Option 1 : \(F(x)=\dfrac{-dU(x)}{dx}\)

Ans: Option 1)

CONCEPT:

• Potential Energy: The energy stored in the body or system by virtue of its configuration or its position is called potential energy.
• Force: Force is the external agency that tends to change the state of motion of a body.
  • It has both magnitude and direction.

EXPLANATION:

• The potential energy is equal to negative work done in shifting an object from some reference point to a given position for conservative force.

In mathematical form, it is given as,

\({\mathrm{d} U(x)}=-F(x){\mathrm{d} x}\)

\(\therefore\)  \(F(x)=\dfrac{-dU(x)}{dx}\) 

where F is the force in newton and dU/dx is change in potential energy per unit length.

The answer is option 1).