Question

In the figure shown there is the plot of a potential energy function of a conservative system $U$ versus $x.$ Which of the following statements is correct ?

• A. The force has the greatest magnitude at point $E_2.$
• B. The force is positive and greater than zero at points $E_1,E_2,E_3$ and $E_4.$
• C. The system is in stable equilibrium
  at $E_3.$
• D. The system is in neutral equilibrium
  at $E_1.$

Answer 1

Answer: (D)

$F=-\frac{\partial U}{\partial x}$
Force $F$ versus x is drawn in Figure. At points $E_1,E_2,E_3$ and $E_4$
$F=0$
$F$ has the greatest magnitude nearer to point $E_1.$
If $U$ is minimum i.e., $\frac{\partial U}{\partial x}=0$ and $\frac{{\partial }^{2}U}{\partial x^2}=$ positive, equilibrium is stable.
If $U$ is maximum i.e., $\frac{\partial U}{\partial x}=0$ and $\frac{{\partial }^{2}U}{\partial x^2}=$ negative, equilibrium is unstable.
If $U$ is constant i.e., $\frac{\partial U}{\partial x}=0$ and $\frac{{\partial }^{2}U}{\partial x^2}=0$ equilibrium is neutral.