Question

For a conservative unidimensional force field $F_x=-\frac{dU}{dx}$. What is the stable equilibrium position?
Information I : $F_x=0$ at $x=2$.
Information II : $\frac{d^{2}U}{d{x}^2}$ is positive at $x=2$.

• A. Question can be solved by information I only.
• B. Question can be solved by information II only.
• C. Question can be solved by information I & II together only.
• D. Question cannot be solved by using these information only.

Answer 1

The correct option is C Question can be solved by information I & II together only.

For stable equilibrium position Force should be zero $F=-\frac{dU}{dx}=0$ and the potential energy curve should be concave upwards i.e. $\frac{d^{2}U}{d{x}^2}$ should be positive.

Hence, both information are required to know the stable equilibrium position.