# Engineering Mechanics Questions and Answers – Moment of a Couple

This set of Engineering Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Moment of a Couple”.

1. Couple is having a combination of two forces. They are different in magnitude.
a) True
b) False

Explanation: The couple is a combination of two forces of the same magnitude. They are acting in the same sense of rotation. That is they are acting in the opposite direction but giving the body a rotation in the same direction. Whether it may be in a clockwise direction or anti-clockwise.

2. Determine the couple moment acting on the beam shown.

a) 500Nm
b) 1500Nm
c) 740Nm
d) 50Nm

Explanation: As we know that the moment is vector quantity, their summation requires vector math. The couple moment is also the same. That is they are also the vectors and requires vector math. Thus the resultant couple moment is the vector sum of the various couples acting in the body.

3. The distance between the forces acting in the couple is ____________
a) Infinity
b) Zero
c) A finite distance
d) A circular loop

Explanation: The distance between the forces acting in the couple is having a finite distance. Couple is the combination of two forces which are acting in the same sense of rotation. That is they are acting in the opposite direction to provide the same direction rotation.

4. The resultant force acting in the couple is _________
a) Zero
b) Infinite
c) Twice the magnitude of the single force
d) Half the magnitude of the single force

Explanation: The resultant of the force acting on the couple is always zero. As the force are acting in the opposite directions. So if we add the forces algebraically then the sum is going to be zero. Or in other words, they cancel each other.
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5. A man is travelling in the car. He is driving the car. If he is taking a turn in the road. He is applying force to the steering wheel by holding the wheel with his both hands. The steering wheel is facing a moment of force.
a) True
b) False

Explanation: The man is trying to rotate the wheel by applying the force. The force is being applied on the steering wheel. Which is rotating the wheel, but it is the moment of the couple. Because the man has holded the wheel with his both hands, hence it is not the moment of the force.

6. Which of the following is correct for the moment of couple M caused by two forces of same magnitude F and are separated by a distance of r?
a) M = rxF
b) M = r.F
c) M = -(rxF)
d) M = -(r.F)

Explanation: The answer is M = rxF. The moment id the cross product of the distance and the forces. It is the direction as directed by the curling of the hand. The thumb representing the direction of the moment. And the motion of the finger, that is the rotation gives the direction of the rotation caused by the forces.

7. A couple moment is a _______ vector.
b) Scalar
c) Del
d) Free

Explanation: A couple moment is a free vector. It can act anywhere between the forces. As the couple is formed by two forces acting in the opposite directions. These forces are separated by a distance r, say, then the moment caused by them can act anywhere in between these forces.

8. Determine the couple moment acting on the beam shown.

a) 20KNm
b) 21KNm
c) 22KNm
d) 19KNm

Explanation: As we know that the moment is vector quantity, their summation requires vector math. The couple moment is also the same. That is they are also the vectors and requires vector math. Thus the resultant couple moment is the vector sum of the various couples acting in the body.

9. Which of the following is correct?
a) The couple moment depends on the axis of rotation
b) The couple moment depends directly on the radius vector of forces
c) The couple moment depends only on the distance vector between the forces
d) The couple moment’s direction is given by the left hand rule

Explanation: The couple moment depends only on the distance vector between the forces. The radius vector of the forces are not making the couple depended over it. But the distance vector is driven by subtracting the radius vectors of the forces. This means that the moment of the couple doesn’t directly depend on the radius vector of forces.

10. If the forces acting on the couple are in the same direction, that is they are not in the opposite direction as always they are, then?
a) The direction of the forces doesn’t determine the moment
b) The couple moment will be maximum
c) The couple is not possible
d) No change occurs

Explanation: The forces are always in the opposite direction for the couple moment. But if they don’t act like the same, that is they change their directions and align themselves in the same direction then the couple is not possible.

11. Determine the couple moment acting on the pipe shown.

a) -130Nm
b) 130Nm
c) -120Nm
d) 120Nm

Explanation: As we know that the moment is vector quantity, their summation requires vector math. The couple moment is also the same. That is they are also the vectors and requires vector math. Thus the resultant couple moment is the vector sum of the various couples acting in the body.

12. The resultant couple moment is ____________ sum of various couples acting on the body.
a) Vector
b) Scalar
c) Scalar Triple
d) Dot

Explanation: As we know that the moment is vector quantity, their summation requires vector math. The couple moment is also the same. That is they are also the vectors and requires vector math. Thus the resultant couple moment is the vector sum of the various couples acting in the body.

13. Determine the couple moment acting on the triangular plane shown.

a) 1600Nm
b) 100Nm
c) 2600Nm
d) 600Nm

Explanation: None.

14. If two forces magnitude F each are acting in the Cartesian coordinate and are acting at the points A(3,3) and B(-3,3). They are heading towards negative z direction and positive z direction respectively. The distance between them is given as r. The radius vectors of the force at A and B are Ra and Rb respectively. Then the moment is given as:
a) (Ra-Rb).F
b) (Rb-Ra).F
c) (Ra-Rb)xF
d) (Rb-Ra)xF

Explanation: The moment of a couple as we know is the cross product of the force and the distance between them. But in this case, we are given the radius vectors of the forces. So when we apply the vector maths to find the distance between the forces we get that the distance r = Rb-Ra. Now that we have the distance, we cross it with the force.

15. Determine the couple moment acting on the pipe shown.

a) 108j + 144k Nm
b) -108j + 144k Nm
c) 108j – 144k Nm
d) -108j – 144k Nm

Explanation: As we know that the moment is vector quantity, their summation requires vector math. The couple moment is also the same. That is they are also the vectors, and requires vector math. Thus the resultant couple moment is the vector sum of the various couples acting in the body.

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