Question

Potential energy of a particle along $x-$axis varies as $U=-20+(x-2{)}^2,$ where $U$ is in joule and $x$ in meter. State the type of equilibrium at $x=2m$.

• A. Stable
• B. Unstable
• C. Neutral
• D. Equilibrium not attained

Answer 1

The correct option is A Stable

For stable equilibrium, $\frac{d^{2}U}{d{x}^2}>0$

For unstable equilibrium, $\frac{d^{2}U}{d{x}^2}<0$

$U=-20+(x-2{)}^2$

for max or min, $\frac{dU}{dx}=2(x-2)=0\Rightarrow x=2$

$\frac{d^{2}U}{d{x}^2}=2>0$

So it is stable equilibrium.