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In case of forces, a couple means
- a)Two unequal forces acting at two points
- b)Two equal and like parallel forces acting at two points
- c)Two equal and perpendicular forces acting at two points
- d)Two equal and opposite forces acting at two points
Correct answer is option 'D'. Can you explain this answer?
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In case of forces, a couple meansa)Two unequal forces acting at two po...
Couple: When the pair of equal parallel forces that are opposite in direction applied on a body then it rotates of tries to rotate about a point or axis is called a couple.
Moment of a couple or couple (C) = P × a
Characteristics of a couple: A couple (whether clockwise or anticlockwise) has the following characteristics:
Moment of a couple or couple (C) = P × a
Characteristics of a couple: A couple (whether clockwise or anticlockwise) has the following characteristics:
- The algebraic sum of the forces, constituting the couple, is zero.
- The algebraic sum of the moments of the forces, constituting the couple, about any point is the same, and equal to the moment of the couple itself.
- A couple cannot be balanced by a single force. But it can be balanced only by a couple of opposite sense.
- Any no. of co-planer couples can be reduced to a single couple, whose magnitude will be equal to the algebraic sum of the moments of all the couples.
Torque (τ): It is a physical quantity, similar to force that causes the rotational motion. It is the cross product of the force with the perpendicular distance between the axis of rotation and the point of application of the force with the force.
⇒ τ = r × F = r F sin θ
Where r = distance from point of application of force (in meter), f = force (in Newton), and θ = angle between
Also, Torque (τ) = r × f = r × F
Where r = component of the distance in the direction perpendicular to the
F = component of the force in the direction perpendicular to
⇒ τ = r × F = r F sin θ
Where r = distance from point of application of force (in meter), f = force (in Newton), and θ = angle between
Also, Torque (τ) = r × f = r × F
Where r = component of the distance in the direction perpendicular to the
F = component of the force in the direction perpendicular to
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In case of forces, a couple meansa)Two unequal forces acting at two po...
Understanding Couples in Mechanics
A couple in mechanics refers to a pair of forces that create a rotational effect without causing any translational motion. Below are the key points to understand why option 'D' is the correct answer.
Definition of a Couple
- A couple consists of two equal and opposite forces that act on a body at different points.
- These forces are equal in magnitude, opposite in direction, and separated by a distance.
Characteristics of Couples
- Equal Forces: The forces must be of the same magnitude.
- Opposite Direction: The forces act in opposite directions, ensuring that their effects do not cancel each other out in terms of translational motion.
- Separation: The forces are applied at two distinct points on the body, creating a moment or torque.
Effect of Couples
- The primary effect of a couple is to produce rotation.
- The moment created by a couple can be calculated as the product of one of the forces and the distance between the lines of action of the forces (the arm of the couple).
Why Other Options are Incorrect
- Option A: Two unequal forces do not create a couple; they can cause translation.
- Option B: While two equal and like parallel forces can create a moment, they do not fulfill the definition of a couple as they do not act in opposite directions.
- Option C: Two equal and perpendicular forces create a net force and do not constitute a couple.
In conclusion, a couple is fundamentally characterized by two equal and opposite forces acting at two distinct points, leading to rotation without translation, making option 'D' the correct choice.
A couple in mechanics refers to a pair of forces that create a rotational effect without causing any translational motion. Below are the key points to understand why option 'D' is the correct answer.
Definition of a Couple
- A couple consists of two equal and opposite forces that act on a body at different points.
- These forces are equal in magnitude, opposite in direction, and separated by a distance.
Characteristics of Couples
- Equal Forces: The forces must be of the same magnitude.
- Opposite Direction: The forces act in opposite directions, ensuring that their effects do not cancel each other out in terms of translational motion.
- Separation: The forces are applied at two distinct points on the body, creating a moment or torque.
Effect of Couples
- The primary effect of a couple is to produce rotation.
- The moment created by a couple can be calculated as the product of one of the forces and the distance between the lines of action of the forces (the arm of the couple).
Why Other Options are Incorrect
- Option A: Two unequal forces do not create a couple; they can cause translation.
- Option B: While two equal and like parallel forces can create a moment, they do not fulfill the definition of a couple as they do not act in opposite directions.
- Option C: Two equal and perpendicular forces create a net force and do not constitute a couple.
In conclusion, a couple is fundamentally characterized by two equal and opposite forces acting at two distinct points, leading to rotation without translation, making option 'D' the correct choice.
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