14 Lecture

Which of the following is not a condition for a rigid body to be in equilibrium?

A) The net force acting on the body is zero

B) The net torque acting on the body is zero

C) The center of mass of the body is at rest

D) The body is not rotating

Answer: D) The body is not rotating

A uniform rod of length 2 meters is balanced horizontally at its midpoint. What is the net torque acting on the rod?

A) Zero

B) mg

C) 2mg

D) 4mg

Answer: A) Zero

A ladder is leaning against a wall. Which of the following forces contribute to the torque acting on the ladder?

A) The force of gravity on the ladder

B) The force of the wall pushing back on the ladder

C) The normal force acting on the ladder

D) Both A and B

Answer: D) Both A and B

Two forces of equal magnitude and opposite direction act on a rigid body. What is the net torque acting on the body?

A) Zero

B) Equal to the magnitude of the forces

C) Double the magnitude of the forces

D) Cannot be determined without knowing the distance between the forces

Answer: A) Zero

What is the relationship between torque and moment arm?

A) Torque is proportional to moment arm

B) Torque is inversely proportional to moment arm

C) Torque is equal to moment arm squared

D) Torque is equal to moment arm cubed

Answer: A) Torque is proportional to the moment arm

A force of 10 N is applied to a wrench with a moment arm of 0.1 meters. What is the torque produced by the force?

A) 0.1 Nm

B) 1 Nm

C) 10 Nm

D) 100 Nm

Answer: B) 1 Nm

An object is in rotational equilibrium if:

A) The net force acting on it is zero

B) The net torque acting on it is zero

C) The object is at rest

D) The object is not rotating

Answer: B) The net torque acting on it is zero

An object is in translational equilibrium if:

A) The net force acting on it is zero

B) The net torque acting on it is zero

C) The object is at rest

D) The object is not rotating

Answer: A) The net force acting on it is zero

A person is holding a weight in one hand. Which of the following forces is producing torque?

A) The force of gravity on the weight

B) The force of the person's hand on the weight

C) The normal force acting on the weight

D) Both A and B

Answer: B) The force of the person's hand on the weight

Which of the following is a condition for rotational equilibrium?

A) The net force acting on the object is zero

B) The object is at rest

C) The net torque acting on the object is zero

D) The object is not rotating

Answer: C) The net torque acting on the object is zero

What is meant by the equilibrium of a rigid body?

Answer: The state of a rigid body when it is at rest and all the forces acting on it are balanced is called the equilibrium of a rigid body.

What are the conditions for the equilibrium of a rigid body?

Answer: The conditions for the equilibrium of a rigid body are:

The net force acting on the body must be zero.

The net torque (or moment) acting on the body about any axis must be zero.

What is meant by the center of gravity of a rigid body?

Answer: The center of gravity of a rigid body is the point where the entire weight of the body can be considered to be concentrated, and the body behaves as if all its weight is acting through this point.

How is the center of gravity of a uniform object located?

Answer: The center of gravity of a uniform object is located at the geometric center of the object.

What is the difference between stable, unstable, and neutral equilibrium?

Answer: In stable equilibrium, if the body is displaced from its equilibrium position, it will tend to return to its original position. In unstable equilibrium, if the body is displaced from its equilibrium position, it will tend to move away from its original position. In neutral equilibrium, if the body is displaced from its equilibrium position, it will remain in its new position.

What is meant by torque or moment of a force?

Answer: The torque or moment of a force is the measure of the force's ability to cause rotational motion. It is the product of the force and the perpendicular distance between the force's line of action and the axis of rotation.

What is the principle of moments?

Answer: The principle of moments states that in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.

How can the weight of an irregularly shaped object be determined?

Answer: The weight of an irregularly shaped object can be determined by suspending it from different points and measuring the angle of the supporting string or rod. The weight can be calculated using the principle of moments.

What is meant by the term 'couple'?

Answer: A couple is a pair of equal and opposite forces acting on a body but not along the same line. It causes the body to rotate without any translational motion.

How can the stability of a structure be increased?

Answer: The stability of a structure can be increased by:

Lowering the center of gravity

Increasing the base area

Providing adequate support

Increasing the weight of the structure at the base.

Equilibrium of Rigid Bodies

The equilibrium of rigid bodies is an important concept in physics that deals with the balance of forces acting on a rigid body. In simpler terms, it refers to a state where a body is at rest or moving with a constant velocity, and the forces acting on it are balanced. The equilibrium of rigid bodies is applicable in various fields, including engineering, architecture, and other sciences. The equilibrium of rigid bodies is based on three principles of mechanics, known as Newton's laws of motion. These laws state that an object will remain in its state of rest or uniform motion in a straight line unless acted upon by an external force. Additionally, the acceleration of an object is directly proportional to the force acting upon it and inversely proportional to its mass. To understand the equilibrium of rigid bodies, we first need to understand the concept of torque. Torque is the measure of the ability of a force to rotate an object around a fixed axis. It is given by the product of the force and the perpendicular distance from the axis of rotation to the point of application of the force. The SI unit of torque is the Newton-meter (N-m). The equilibrium of rigid bodies can be classified into two types - static equilibrium and dynamic equilibrium. In static equilibrium, a rigid body is at rest, and the net torque acting on it is zero. This means that the sum of all the torques acting on the body must be equal to zero. In dynamic equilibrium, a rigid body is moving with a constant velocity, and the net force and net torque acting on it are both zero. To determine whether a rigid body is in equilibrium, we use the principle of moments. The principle of moments states that the sum of the moments of the forces acting on a body about any point is equal to zero. By choosing an appropriate point, we can simplify the calculations required to determine whether a body is in equilibrium or not. To apply the principle of moments, we need to identify all the forces acting on the body and their directions. We also need to determine the distance of the line of action of each force from the chosen point. Once we have this information, we can calculate the moment of each force and add them up. If the sum of the moments is equal to zero, the body is in equilibrium. If not, then the body is not in equilibrium, and it will either be at rest or in motion. In summary, the equilibrium of rigid bodies is an important concept in physics that is applicable in many fields. It is based on the principles of mechanics and torque, and it can be classified into static and dynamic equilibrium. To determine whether a body is in equilibrium, we use the principle of moments, which states that the sum of the moments of the forces acting on a body about any point is equal to zero.