Test: Moment Of A Couple - Civil Engineering (CE) MCQ

The couple is a combination of two forces of 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 clockwise direction or anti-clockwise.

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 a same direction rotation.

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.

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.

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.

A couple moment is a free vector. It can be 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.

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.

• Force F acting at a distance of 0.9 m.
• A 2 kN force acting at a distance of 10.3 m.
• A 2 kN force acting at a distance of 0.3 m from point Q .

We need to calculate the total couple moment by summing the moments generated by each of the forces.

The total couple moment acting on the beam is approximately 20.9 kNm.

Since this is closest to 20 kNm, the correct answer is: 20 KNm

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, moment of the couple doesn’t directly depends on the radius vector of forces.

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.

The force of 25 N acts at points P and C. The distance between them is 8 m along the z-axis and 6 m along the y-axis.

The vector components for the forces at P and C are:

Force at point P: 25 N
Position vector from point C to point P is r = 6j + 8k

Calculate the Moment (Torque) about point C: The couple moment M can be calculated using the formula:
M = r × F
where r is the position vector and F is the force vector.

Force Vector Components: The force is applied at a 30° angle to the x-axis. To break it into components, we use:
Fx = 25 cos(30°), Fy = 25 sin(30°)

Cross Product Calculation: Using the position vector r = 6j + 8k and force components Fx and Fy,

we can find the couple moment as the cross product.

The calculated couple moment acting on the pipe is approximately -130 Nm.

So, the correct answer is: a) -130Nm.

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.

The moment of 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.

Rate of change of velocity is known as acceleration. Its unit is m/s².
a = change in velocity/time.

Equations of motion:

• v = u + at
• v² = u² + 2as
• s = ut + ½ at²

Given:
u = 36 km/h = 10 m/s
s = 125 m
v = 54 km/h = 15 m/s
t = ?

Using the equation:
v² = u² + 2as

Substitute the given values:
(15)² = (10)² + 2 × a × 125
225 = 100 + 250a
125 = 250a
a = 125 / 250 = 0.5 m/s²

Now use v = u + at:
15 = 10 + (0.5) × t
t = (15 - 10) / 0.5 = 5 / 0.5 = 10 seconds

Answer:
Time taken to cover the distance = 10 seconds.