**Q.13: Define equilibrium? What are the kinds of equilibrium?**

**Ans: EQUILIBRIUM:**

When the resultant of all the forces acting on a body comes to zero the body is said to be in the state of equilibrium.

**Kinds Of Equilibrium:**

There are two kinds of equilibrium.

- Static Equilibrium
- Dynamic Equilibrium

**Q.14: Define static and dynamic equilibrium with examples?**

**Ans: STATIC EQUILIBRIUM:**

A body at rest is said to be in the state of static equilibrium.

**Example**:

Consider a spherical ball of weight 5N suspended from the ceiling by a string. The ball is in static equilibrium. Two forces are acting on the ball: The force of gravity W = SN acting down ward and the tension “T” In the string acting upwards W = T. It means the two forces acting downwards and upwards balance each other so the body is at rest.

**DYNAMIC EQUILIBRIUM:**

If a body has uniform motion along a straight line is said to be in dynamic equilibrium.

**Example:**

When a paratrooper jumps from an aero plane, it moves downward with an acceleration due to gravity. When the parachute opens, an upwards force due to reaction of air acts on the parachute. The force of gravity acting downward is balanced by the air reaction acting upwards so the paratrooper falls down with a uniform velocity.

**Q.16: Write down the three states of Equilibrium? Give examples of each?
(a) stable hi**

Ans: THERE ARE THREE STATES OF equilibrium

- Stable
- Unstable
- Neutral

**Stable Equilibrium:**

A body is said to be in stable equilibrium if it comes back to its original position when it is slightly displaced. in the state of stable equilibrium the center of gravity is raised.

**Examples**:

A cone is standing on its base, as shown in figure (a).

- When this cone is displaced its center of gravity is raised.
- The center of gravity of the cone is near the base.
- A cone in stable equilibrium should have its center of gravity as low as possible.
- The vertical line through its center of gravity is within the base and a torque due to weight of the cone brings it back to the original position.

**Unstable Equilibrium:**

A body is said to be in unstable equilibrium if it does not come back to its original position when it is slightly displaced. The center of gravity is lowered in unstable equilibrium.

**Examples:**

A cone balanced on its apex is unstble equilibrium as shown in figure (b).

- When this cone is disturbed its center of gravity is lowered.
- The vertical line through its center of gravity is outside the base.
- The torque due to weight of the cone toppled the cone down so the one does not regain its original position.

**Neutral State Of Equilibrium:**

A body is said to be in neutral equilibrium if on being slightly displaced, it does not come back to its original position but occupies a new position similar to its original position. The center of gravity of the body remains at the same height.

**Example:**

A cone resting on its side as shown figure (c) is in neutral equilibrium.

It the cone is pushed slightly its center of gravity is neither raised nor lowered but it remains at the same height.

**Q.1: Define circular motion and give any two examples?**

**Ans: CIRCULAR MOTION:**

When a body moves on the circumference of the circle is called circular motion.

**Examples:**

- The rotation of our earth and other planets around the sun.
- The wheel of moving bicycle.

**Q.2: Define uniform circular motion? Explain it with one example?**

Ans: UNIFORM CIRCULAR MOTION:

When a body moves in a circular path with constant speed it is said to be in uniform circular motion.

**Explanation:**

- At any point on the circle the direction of velocity is directed along the tangent to the circle at the point.
- if at any point a body is made free of force it will move tangential to the circle at that point.
- But as the body is moving along the circumference of the circle there must be a force acting towards the center of the circle and this force is called centripetal force.

**Example:**

Consider a body revolving in a circle of radius “r’. Suppose the body be at point “P” initially. After some interval of time it moves to position P. The angle < POP or “0” subtended at the center of circle represents the turning of body during angular displacement.

**Unit:**

The unit of angular displacement is radian.

**Definition Of Radian:**

One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

**1 radian = 57.30°**

**Q.7: Write down the factors on which centripetal force depends?**

Ans: There are the following factors on which centripetal force depends:

- The centripetal force Increases with increasing mass of the body.
- It increases with the square of the velocity of the body.
- It decreases with the increase in the radius of the circular path.

**Q.8: Write down the factors on which centripetal acceleration depends?**

**Ans: CENTRIPETAL ACCELERATION DEPENDS ON THE FOLLOWING FACTORS:**

- The centripetal acceleration is directly proportional to the square of its velocity.
- The centripetal acceleration is inversely proportional to the radius of the circle.