# Worksheet: Moment of a Couple

In this worksheet, we will practice calculating the moment of a couple of two forces and the resultant of two or more couples.

**Q1: **

The two forces and are acting at the points and respectively. Given that they are forming a couple, determine the vector of the couple moment.

- A
- B
- C
- D

**Q3: **

is square having a side length of 3 cm. and belong to , where . Given that two equal forces, each of magnitude 5 N, are acting along and respectively, find the magnitude of the moment of the couple.

- A Nā cm
- B Nā cm
- C Nā cm
- D Nā cm

**Q4: **

is a square of side length 8 cm, where two forces of magnitudes 21 N are acting at and respectively, and their lines of action are in the direction of and respectively. Determine the magnitude of the moment of the couple.

- A Nā cm
- B336 Nā cm
- C Nā cm
- D168 Nā cm

**Q5: **

What is a couple?

- Aa pair of parallel forces with equal magnitude and the same line of action
- Ba pair of forces with equal magnitude
- Ca pair of parallel forces with equal magnitude and opposite direction which do not lie on the same line of action.
- Da pair of forces with the same magnitude and direction.

**Q6: **

is a rectangle, in which and . Two forces of the same magnitude N are acting at and in the directions of and respectively. Determine the magnitude of the moment of the couple.

**Q7: **

is a parallelogram, where , , and the perpendicular distance between and is 6 cm. Given that two forces of the same magnitude 50 N are acting along and , respectively, determine the magnitude of the moment of the couple.

**Q8: **

is a regular hexagon with sides of length 5 cm. Two forces of the same magnitude 13 N are acting along and , respectively. Determine the magnitude of the moment of the couple.

- A130 Nā cm
- B Nā cm
- C Nā cm
- D65 Nā cm

**Q9: **

In the figure below, and and form a couple. Find the algebraic measure of the moment of that couple.

**Q10: **

The given figure shows two forces each of magnitude 267 newtons acting on two edges of a lamina in the form of a rectangle with dimensions and . Find the moment of the couple if .

**Q11: **

Given two forces in a couple, what is the name given to the product of the magnitude of one of the forces and the perpendicular distance between the two forces?

- Athe magnitude of the couple
- Bthe moment of the couple
- Cthe moment of one force of the two forces of the couple
- Dthe resultant of the couple

**Q12: **

is a parallelogram, where and . If two forces of the same magnitude 50 N are acting at and respectively, determine the magnitude of the moment of the couple, rounding your answer to two decimal places.

**Q13: **

is a rhombus in which its diagonal and . Given that two equal forces, each of magnitude 45 N, are acting along and respectively, find the magnitude of the moment of the couple rounded to two decimal places if necessary.

**Q14: **

is a square having a side length of 24 cm, , and , where . Given that two forces, each of magnitude 34.2 N are acting along and , respectively, find the magnitude of the moment of the couple.

- A369.36 Nā cm
- B164.16 Nā cm
- C492.48 Nā cm
- D123.12 Nā cm

**Q15: **

is a regular hexagon, having a side length of 5 cm, where a force of magnitude 15 N is acting along , and another force of the same magnitude is acting at in the direction of . Determine the magnitude of the moment of the couple.

**Q16: **

is a rhombus, where its diagonals and are 13 cm and 7 cm respectively, and two forces of the same magnitude 23 N are acting along and . Determine the magnitude of the moment of the couple, rounding your answer to two decimal places if necessary.

- A283.51 Nā cm
- B141.76 Nā cm
- C299 Nā cm
- D86.29 Nā cm

**Q17: **

If the norm of the moment of a couple is 750 Nā m, and the magnitude of one of its two forces is 50 N, determine the length of the moment arm.

**Q18: **

and are two parallel chords in a circle whose radius is 25 cm, and they are at different distances away from the circleās center, where , and . Given that two forces of the same magnitude 20 N are acting along and , respectively, determine the magnitude of the moment of the couple.

**Q19: **

is an isosceles trapezium, where , , and . Two forces, each of magnitude 50 N, are acting along and . Find the magnitude of the moment of the couple rounded to two decimal places, giving your answer in Nā cm.

**Q20: **

A light rod , which has a length of 22 cm and a mid-point , is under the action of two forces measured in newtons as shown in the figure. Given that a moment of magnitude 22 Nā cm is acting on the rod, determine the moment of the resultant couple acting on the rod.

**Q21: **

If the two forces and form a couple, then find the value of .

**Q22: **

Given that the forces , , and are acting at the points , , and respectively, where the system of forces is equivalent to a couple, , and , determine the magnitude of the moment of the couple.

**Q23: **

Given that and are two forces which form a couple, where , determine .

- A
- B
- C
- D

**Q24: **

is a right-angled triangle at , where and . The two forces and , measured in newtons, are acting on the sides of the triangle as shown in the figure below. If the system of forces is equivalent to a couple, determine the magnitudes of and .

- A ,
- B ,
- C ,
- D ,

**Q25: **

The two forces and are acting at the points and respectively. Given that they are forming a couple, determine the vector of the couple moment.

- A
- B
- C
- D