Types of Equilibrium – What is Equilibrium? – eSaral

Hey, Do you want to learn about the Types of Equilibrium? If so. Then you are at the right place.

## What is Equilibrium?

A body is said to be in translatory equilibrium if the net force acting on the body is zero, $\overrightarrow{\mathrm{F}}_{\text {net }}=0$

If the force are conservative then $\mathrm{F}=-\frac{\mathrm{dU}}{\mathrm{dr}}$

For equilibrium F = 0.

So, $-\frac{d U}{d r}=0$

Or

$\frac{\mathrm{dU}}{\mathrm{dr}}=0$

At equilibrium position slope of U-r graph is zero or the potential energy is optimum (maximum or minimum or constant).

## Types of Equilibrium.

1. Stable Equilibrium
2. Unstable Equilibrium
3. Neutral Equilibrium

### Stable Equilibrium:

When a particle is slightly displaced from equilibrium and it tends to come back towards equilibrium then it is said to be in stable equilibrium

### Unstable Equilibrium:

When a particle is displaced from equilibrium and it tends to move away from equilibrium position then it is said to be in unstable equilibrium

### Neutral Equilibrium:

When a particle is displaced from equilibrium and no force acts on it then the equilibrium is said to be neutral equilibrium

The situation where F = 0 and $\frac{\mathrm{d} \mathrm{U}}{\mathrm{dr}}=0$ can be obtained under three conditions. Three identical balls are placed in equilibrium in positions as shown in fig. (a), (b), and (c) respectively.

1. The ball is placed inside a smooth spherical shell. This ball is in a stable equilibrium position.
2. The ball is placed over a smooth sphere. This is in the Unstable equilibrium position.
3. The ball is placed on smooth horizontal ground. This ball is in the Neutral equilibrium position.