# Stability & States of Equilibrium

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## Stability

Stability refers to the ability of a body to restore to its original static equilibrium, after it has been slightly displaced.

## States of Equilibrium

### Stable Equilibrium

A equilibrium is said to be stable if small, externally induced displacements from that state produce forces or torques that tend to oppose the displacement and return the body to its original equilibrium.

Example: A hanging pendulum or a brick lying on a level plane.

### Unstable Equilibrium

An equilibrium is said to be unstable if the least departures produce forces or torques that tend to increase the displacement.

Example: A rule standing on its end or a ball standing on top of an inverted bowl.

### Neutral Equilibrium

An equilibrium is said to be neutral if small, externally induced displacements from that state does not produce any unbalanced forces or torques that tend to oppose or aggravate the displacement and the body remains in its new equilibrium.

Example: A ball or a pencil lying on a level surface.

## Criteria Of Stable Bodies

Stable bodies tend to have:

Hence, the stablity of an object can be improved by:

• Lowering its centre of gravity
• Increasing the base area

## Worked Examples

### Example 1

Where does the centre of gravity lie for a

1. uniform ruler
2. sphere of uniform density?

a. Uniform Ruler: For a uniform ruler, the point at which its entire mass can be considered concentrated is at the geometric center of the ruler.

b. Sphere of Uniform Density: In the case of a sphere with uniform density, the center of gravity is at the exact center of the sphere, regardless of its external shape or size.

### Example 2

1. When does an object topple?
2. How can the stability of an object be increased?

a. When does an object topple? An object topples when the center of gravity moves beyond the base of support. If the vertical projection of the center of gravity falls outside the footprint of the object’s base, it becomes unstable, leading to toppling.

b. How can the stability of an object be increased? To enhance the stability of an object, the center of gravity must be kept low and within the base of support. This can be achieved by widening the base, distributing mass uniformly, or lowering the overall center of gravity. Additionally, increasing friction between the object and its support surface contributes to greater stability.

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