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.
- Stable Equilibrium
- Unstable Equilibrium
- 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.
- The ball is placed inside a smooth spherical shell. This ball is in a stable equilibrium position.
- The ball is placed over a smooth sphere. This is in the Unstable equilibrium position.
- The ball is placed on smooth horizontal ground. This ball is in the Neutral equilibrium position.
Difference Between Stable, Unstable, and Neutral Equilibrium
| S.no | Stable equilibrium | Unstable equilibrium | Neutral equilibrium |
| 1 | Net force is zero | Net force is zero | Net force is zero |
| 2 | $\frac{d U}{d r}=0$ or slope of $U-r$ graph is zero | $\frac{\mathrm{dU}}{\mathrm{dr}}=0$ or slope of U-r graph is zero. | $\frac{\mathrm{dU}}{\mathrm{dr}}=0$ or slope of U-r graph is zero. |
| 3 | When displaced slightly, from its equilibrium position a net restoring force starts acting on the body which has a tendency to bring the body back to its equilibrium position. | When displaced slightly from its equilibrium position, a net force starts acting on the body which moves the body in the direction of displacement or away from the equilibrium position. | When displaced slightly from its equilibrium position the body has neither the tendency to come back to original position nor to move away from the original position. |
| 4 | Potential energy in equilibrium position is minimum as compared to its neighboring points or $\frac{\mathrm{d}^{2} U}{\mathrm{dr}^{2}}=$ positive |
Potential energy in equilibrium position is maximum as compared to its neighboring points or $\frac{d^{2} U}{d r^{2}}=$ negative |
Potential energy remains constant even if the body is displaced from its equilibrium position. or $\frac{d^{2} U}{d r^{2}}=0$ |
| 5 | When displaced from equilirbium position the centre of gravity of the body goes up. |
When displaced from equilibrium position the centre of gravity of the body comes down. | When displaced from equilibrium position the centre of gravity of the body remains at the same level. |
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