Equilibrium in Physics - Class XI

All of the above
Impulse = Force$\times$time = $m\Delta{v}$ = Momentum
A body will be at rest for a moment when it changes direction.
When a body is in equilibrium it always has minimum potential energy and no force is acting upon it.
Force is a vector quantity and hence its direction will result in different force quantity.

When an object is not in equilibrium, net force acting on the body is not zero.
Therefore when some force acts on the object, it is in accelerated motion because, $F= ma$

The equilibrium is of two types
(1) Static equilibrium
(2) Dynamic equilibrium
When a body remains in the state of rest under the influence of the applied forces, the body is in static equilibrium.

A body is said to be in translatory equilibrium when net external force acting on it is zero.

The forces which are acting at a point are called concurrent forces. These forces are said to be in equilibrium, when the resultant is zero.

Two forces acting at a point will be in equilibrium.

The resultant of all the forces acting the body should be equal to zero. The resultant moment of all the forces acting on the body about the point of rotation should be zero.

When a body remains in the same state of motion (translational or rotational) under the influence of the applied forces, the body is said to be dynamic equilibrium.

Stable equilibrium means that, with small deviations of the body from this state, forces or moments of forces emerge which tend to return the body to the state of equilibrium. A ball located at the bottom of a spherical deepening is in a state of stable equilibrium.

There are three states of equilibrium.

Unstable equilibrium means that, with a small deviation of the body from the equilibrium state, forces emerge which tend to increase this deviation. A ball located at the top of a spherical projection is an example of unstable equilibrium. 

If a pencil standing vertically is slightly disturbed from its position it will not come back to its original position. This type of equilibrium is called unstable equilibrium, other example of unstable equilibrium are vertically standing cylinder and funnel etc.

When a body remains in the same state of motion (translational or rotational) under the influence of the applied forces, the body is said to be dynamic equilibrium.

When the center of gravity of a body lies below point of suspension or support, the body is said to be in stable equilibrium. For example a book lying on a table is in stable equilibrium.A book lying on a horizontal surface is an example of stable equilibrium. If the book is lifted from one edge and then allowed to fall, it will come back to its original position.
Other examples of stable equilibrium are bodies lying on the floor such as chair, table etc.

The resultant moment of all the forces acting on the body about the point of rotation should be zero, i.e., the sum of the anticlockwise moments about the axis of rotation must be equal to the sum of the clockwise moments about the same axis.

It's center of gravity is neither raised nor lowered. This means that its center of gravity is at the same height as before this type of equilibrium is known as neutral equilibrium.

When the center of gravity of a body lies at the point of suspension or support, the body is said to be in neutral equilibrium. Example: rolling ball.If the ball is pushed slightly to roll, it will neither come back to its original nor it will roll forward rather it will remain at rest. This type of equilibrium is called neutral equilibrium.

Both the above options are conditions for a body to be on equilibrium and for equilibrium, sum of anticlockwise moments about the axis of rotation must be equal to the sum of clockwise moments about the same axis.

When the center of gravity of a body lies below point of suspension or support, the body is said to be in stable equilibrium. For example a book lying on a table is in stable equilibrium.

An object is said to be in equilibrium when there is no resultant force acting on the object, the total clockwise moments about any point is equal to the total anticlockwise moments about the same point.

A sleeping cat, a flask resting on a table and winding a clock are the objects is / are in equilibrium.

Potential energy at extreme position = kinetic energy at mean position

$mg\ell (1-cos\theta )=\frac { 1 }{ 2 } m{ v }^{ 2 }$

At equilibrium, the force F = -dU/dr = 0. Differentiating U = A/r^6 - B/r^12 gives -6A/r^7 + 12B/r^13 = 0, so r^6 = 2B/A. Substituting this back into U gives A/(2B/A) - B/(2B/A)^2 = A^2/2B - B * A^2/4B^2 = A^2/2B - A^2/4B = A^2/4B.

For an object to be in stable equilibrium, its center of gravity must be positioned such that the vertical line passing through it falls within the base of support.