Equilibrium (Chapter # 06) Physics 10th - Question Answers

Physics 10th - Question Answers

Equilibrium (Chapter # 06)

Q.1: Define Parallel Forces?

Ans: Parallel forces can be defined as: “When a number of forces act on a body and if their directions are parallel, they are called parallel forces.”

Q.2: What do you understand by two like and unlike parallel forces?

Like Parallel Forces: If two parallel forces have the same direction, they are called like parallel forces.

Examples: “Consider two like parallel forces $F_1$ and $F_2$ acting on a body at points 'A' and 'B'. Suppose $\vec{R}$ is the resultant force of $F_1$ and $F_2$, then:

$$\vec{R} = F_1 + F_2$$

Unlike Parallel Forces: If two parallel forces have opposite directions, they are called unlike parallel forces.

Examples: “Consider two unlike parallel forces $F_1$ and $F_2$ acting on a body at points 'A' and 'B'. Suppose $\vec{R}$ is the resultant force of $F_1$ and $F_2$. Here, $F_1$ is greater than $F_2$, then:

$$\vec{R} = F_1 - F_2$$

Q.3: Define the axis of rotation. Give any one example.

Ans: Axis of Rotation: Some bodies cannot move from place but can rotate about a fixed line or axis, called its axis of rotation. A force acting on such a body produces rotation only.

Example: When we apply a force on a door, it rotates because it cannot move as a whole along a straight line. The axis about which the body rotates is called the axis of rotation.

Q.4: Define Moment Arm?

Ans: The moment arm can be defined as: “It is the perpendicular distance between the axis of rotation and the line of the action of the forces.”

Q.5: Define Torque or Moment? Write down its formula and units.

Ans: Torque or Moment: The turning effect of a force on a body is called torque or moment of force. It is equal to the product of the force and the moment arm.

Formula:

$$\text{Torque} = \text{Force} \times \text{Moment Arm}$$ $$\tau = F \times r$$

Where:

• $\tau$ (Tau) = Torque
• $F$ = Applied Force
• $r$ = Moment Arm (It is a vector quantity)

Unit of Torque or Moment: The S.I. unit of torque is Newton-meter (Nm).

Q.6: Write down the factors on which torque depends.

Ans: Torque Depends on the Following Factors:

• Torque is directly proportional to the applied force.
• Torque is directly proportional to the moment arm.

Q.7: Define Center of Gravity.

Ans: The center of gravity is the point inside or outside the body where the whole weight of the body appears to act.

Q.8: Write down the position of the center of gravity of the following objects.

Ans: Position of Center of Gravity:

• Uniform Rod
• Plate (square, rectangle, or parallelogram in shape)

Objects and Positions of Center of Gravity:

• Rectangular block or cube: Intersection of diagonals
• Circular plate: Center of the plate
• Triangular plate: Intersection of medians
• Cylinder: Midpoint of axis

Name of Object	Position of Center of Gravity
Uniform Rod	Center of the rod
Circular Plate	Center of the plate
Plate (square, rectangle, or parallelogram)	Intersection of lines joining midpoints
Triangular Plate	Intersection of medians
Rectangular Block or Cube	Intersection of diagonals
Cylinder	Midpoint of axis

Q.9: How can we find the center of gravity of an irregularly shaped body?

Ans: We can find the center of gravity of an irregularly shaped body using a plumb line. A plumb line is a device that helps locate the center of gravity easily. There are two forces acting on the plumb line:

• Weight of the plumb line
• Tension in the string

Q.10: How can you find the center of gravity of an irregular metal sheet or card sheet?

Ans: A simple method can be used to find the center of gravity of irregularly shaped bodies:

1. Drill three small holes near the edge of the plate whose center of gravity is to be determined.
2. Suspend the plate from a nail fixed horizontally in a wall using one of the holes, say "A".
3. When the plate is at rest, suspend a plumb line from the nail. Draw a line “Aa” on the plate along the plumb line.
4. The center of gravity lies somewhere on the line “Aa”.

Procedure for Finding Center of Gravity:

Repeat the procedure with hole "B" on the nail. Again, the center of gravity must lie somewhere on the line "Bb". The only common point on the lines "Aa" and "Bb" is the center of gravity. If the plate is suspended using the third hole "C," the line will also pass through point "G".

Q.11: What is a Couple? Calculate the Moment of the Couple.

Ans: Couple of Forces: A couple is a pair of equal, parallel, and unlike forces having different lines of action.

Calculation of Moment of Couple: Consider two equal unlike parallel forces, each of magnitude $F$, acting at points "A" and "B". The torques or moments of these two forces are given by:

• The moment of the force $F$ at A: $F \times OA$
• The moment of the force $F$ at B: $F \times OB$

Both moments have the same direction (counterclockwise). Thus, the total moment of the couple is the sum of the two moments.

$$\text{Moment of the couple} = F \times OA + F \times OB$$$$= F \times (OA + OB)$$$$= F \times AB$$

Moment of a Couple:

The moment of the couple is equal to the product of one of the forces and the perpendicular distance between the lines of action of the two forces. This perpendicular distance is called the arm of the couple.

Thus, the torque or moment of a couple is the product of either force and the arm of the couple. Whenever a couple acts on a body, there is only rotation. It should be noted that a couple cannot be balanced by a single force; it can only be balanced by an equal and opposite couple.

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

Ans: Equilibrium: When the resultant of all the forces acting on a body is zero, the body is said to be in a state of equilibrium.

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 act on the ball: the force of gravity $W = 5N$ acting downward and the tension $T$ in the string acting upward ($W = T$). The downward and upward forces balance each other, so the body is at rest.

Dynamic Equilibrium: A body in uniform motion along a straight line is said to be in dynamic equilibrium.

Example: When a paratrooper jumps from an airplane, they move downward with an acceleration due to gravity. When the parachute opens, an upward force due to the reaction of air acts on the parachute. The force of gravity acting downward is balanced by the air resistance acting upward, so the paratrooper falls with a uniform velocity.

Q.15: Define Equilibrium. Write down Its Two Conditions.

Ans: Equilibrium: A body at rest or moving with uniform velocity along a straight line is in a state of equilibrium.

Conditions of Equilibrium:

1. First Condition of Equilibrium:

   • The sum of all forces acting upon a body is equal to zero.
   $$\sum \vec{F} = \vec{F_1} + \vec{F_2} + \vec{F_3} + \ldots = 0$$
   • Along the x-axis:
   $$\sum F_x = 0$$
   • Along the y-axis:
   $$\sum F_y = 0$$

2. Second Condition of Equilibrium:

   • The sum of all torques acting upon a body is always equal to zero.
   $$\sum \tau = \tau_1 + \tau_2 + \tau_3 + \ldots = 0$$

Q.16: Write down the Three States of Equilibrium. Give Examples of Each.

Ans: Three States of Equilibrium:

1. Stable Equilibrium:
• A body is said to be in stable equilibrium if it returns to its original position when slightly displaced. In this state, the center of gravity is raised.

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 the weight of the cone brings it back to its original position.

Unstable Equilibrium:

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

Examples:

• A cone balanced on its apex is in unstable equilibrium, as shown in figure (b).
  • When the 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 the weight of the cone causes it to topple down, preventing it from regaining its original position.

Neutral State of Equilibrium:

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

Example:

• A cone resting on its side, as shown in figure (c), is in neutral equilibrium.
  • If the cone is pushed slightly, its center of gravity is neither raised nor lowered but remains at the same height.