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Standard XII

Physics

Conservative Force as Gradient of Potential

Potential ene...

Question

Potential energy $U (x)$ and associated force $F (x)$ bear the relation $F (x) = \frac{- d U (x)}{d x}$ . Dependence of potential energy of a two-particle system on the separation $x$ between them is shown in the following figure.

Which of the following graphs shows the correct variation of force $F (x)$ with $x$ ?

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Solution

The correct option is A
$F (x) = - d U (x) / d x = -$ slope of $U (x) - x$ curve.
Initially, slope is constant and positive until $x = a$ . So, force is constant (negative) till that point. After that the slope of $U - x$ curve becomes zero, so the force becomes zero after $x = a$ .

Option (a) matches this description.

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Potential energy U(x) and associated force F(x) bear the relation F(x)=−dU(x)dx. Dependence of potential energy of a two-particle system on the separation x between them is shown in the following figure. Which of the following graphs shows the correct variation of force F(x) with x?

The correct option is A F(x)=−dU(x)/dx=− slope of U(x)−x curve. Initially, slope is constant and positive until x=a. So, force is constant (negative) till that point. After that the slope of U−x curve becomes zero, so the force becomes zero after x=a. Option (a) matches this description.