**Q3: **

Parallel forces , , , and act at the points , , , and , respectively, where the forces are in equilibrium. Given that and N, and they act in the opposite direction of , find each of , , and .

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

**Q4: **

Three coplanar parallel forces having magnitudes of 6, 8, and newtons are acting at collinear points , , and respectively. , and is not between and . The first two forces are acting in opposite directions, and the resultant of the three forces has a magnitude of 6 N, acting in the direction of the second force, with its line of action intersecting at a point , where . Find the magnitude of and the length of .

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

**Q5: **

A uniform rod having a weight of 64 N and a length of 168 cm is resting horizontally on two identical supports at its ends. A weight of magnitude 56 N is suspended at a point on the rod that is cm away from . If the magnitude of the reaction at is double that at , determine the value of .

**Q6: **

A uniform rod having a weight of 35 N is resting horizontally on two supports and at its ends, where the distance between the supports is 48 cm. If a weight of magnitude 24 N is suspended at a point that is 38 cm away from , determine the reactions of the two supports and .

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

**Q7: **

A non-uniform rod having a weight of 40 N and a length of 80 cm is suspended vertically from its midpoint by a light string, and it becomes in equilibrium in a horizontal position when a weight of magnitude 29 N is suspended from its end . Determine the distance between the point at which the weight of the rod is acting and end . After removing the weight at , determine the magnitude of the vertical force that would be needed to keep the rod in equilibrium in a horizontal position when it acts at end .

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

**Q8: **

A uniform rod having a length of 1.3 m and weighing 147 N is resting in a horizontal position on two supports, where the support is at the end , and is at a distance from the end . Find the reaction of the support and the distance , given that .

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

**Q9: **

A uniform rod weighs 15 N and has a length of 90 cm. It is suspended from its ends by two vertical strings, where is the tension of the string at , and is the tension of the string at . A weight of 14 N is suspended from the rod, 30 cm away from , and a weight of 27 N and is suspended from the rod, 30 cm away from . Determine the values of and .

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

**Q10: **

is a uniform rod having a length of 111 cm and weighing 78 N. The rod is suspended horizontally from its ends and by two vertical strings. Given that a weight of 111 N is suspended cm away from the end so that the tension at is twice that at , determine the tension at and the value of .

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

**Q11: **

is a uniform rod having a length of 78 cm and weighing 155 N. The rod is resting horizontally on two supports, and , where is 13 cm away from . Determine the minimum weight to be suspended at so that there is no pressure at , and find out the pressure on at that instant.

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

**Q12: **

is a uniform rod with length 48 cm and weight 20 kg-wt. It rests in a horizontal position on two supports, and , that are 6 cm and 12 cm away from and , respectively. A weight of magnitude 26 kg-wt is suspended from the rod at a point 12 cm away from . Another weight of 16 kg-wt is suspended from the rod, 18 cm away from . Calculate the size of the reaction forces, and , at and respectively.

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

**Q13: **

The points , , , , and are lying on the same straight line, where . Four parallel forces of magnitudes 14, 19, , and 20 newtons are acting at , , , and respectively. If their resultant passes through point , calculate the size of force , giving your answer in newtons.

- A
- B
- C
- D
- E

**Q14: **

The points , , , , and are lying on the same straight line, where . Four parallel forces of magnitudes 19, 8, , and 15 newtons are acting at , , , and respectively. If their resultant passes through point , calculate the size of force , giving your answer in newtons.

- A
- B
- C
- D
- E

**Q15: **

The points , , , , and are lying on the same straight line, where . Four parallel forces of magnitudes 16, 19, , and 18 newtons are acting at , , , and respectively. If their resultant passes through point , calculate the size of force , giving your answer in newtons.

- A
- B
- C
- D
- E

**Q16: **

, , , , and are five points on the same straight line, where , , , and . Forces of magnitudes 4, , and 10 newtons are acting vertically downwards at the points , , and respectively, and forces of magnitudes 7 and newtons are acting vertically upwards at and respectively. Given that the resultant of the forces is 3 N, and it is acting vertically downwards at the point , where and , determine the values of and .

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

**Q17: **

, , , , and are five points on the same straight line, where , , , and . Forces of magnitudes 2, , and 9 newtons are acting vertically downwards at the points , , and respectively, and forces of magnitudes 4 and newtons are acting vertically upwards at and respectively. Given that the resultant of the forces is 1 N, and it is acting vertically downwards at the point , where and , determine the values of and .

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

**Q18: **

Four parallel forces of magnitudes 6, 3, 8, and 2 kg-wt are acting perpendicularly in the same direction on the points , , , and respectively. Given that the four points are on the same straight line, where and , determine the magnitude and direction of the resultant force and the distance between the resultantβs point of action on the straight line and .

- A , in the same direction of the forces,
- B , in the opposite direction to the forces,
- C , in the opposite direction to the forces,
- D , in the same direction of the forces,
- E , in the same direction of the forces,

**Q19: **

Four parallel forces of magnitudes 4, 8, 5, and 1 kg-wt are acting perpendicularly in the same direction on the points , , , and respectively. Given that the four points are on the same straight line, where and , determine the magnitude and direction of the resultant force and the distance between the resultantβs point of action on the straight line and .

- A , in the same direction of the forces,
- B , in the opposite direction to the forces,
- C , in the opposite direction to the forces,
- D , in the same direction of the forces,
- E , in the same direction of the forces,

**Q20: **

Points , , , , and lying in the same straight line, such that , , , and . Five forces of magnitudes 40, 25, 20, 45, and 50 newtons are acting as shown in the figure. Determine their resultant and the distance between its line of action and point .

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

**Q21: **

Points , , , , and lying in the same straight line, such that , , , and . Five forces of magnitudes 20, 35, 40, 45, and 35 newtons are acting as shown in the figure. Determine their resultant and the distance between its line of action and point .

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

**Q22: **

Points , , , , and lying in the same straight line, such that , , , and . Five forces of magnitudes 25, 40, 20, 50, and 35 newtons are acting as shown in the figure. Determine their resultant and the distance between its line of action and point .

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

**Q23: **

Points , , , , and lying in the same straight line, such that , , , and . Five forces of magnitudes 30, 30, 45, 25, and 25 newtons are acting as shown in the figure. Determine their resultant and the distance between its line of action and point .

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

**Q24: **

, , and are three points on one straight line, where , , and . Forces of magnitudes 2 N and 2 N are acting vertically downward at the two points and , respectively, and a force having a magnitude of 7 N is acting vertically upward at the point . Find the magnitude and direction of the resultant and the distance of its point of action from the point .

- A ,upward,
- B , downward,
- C , downward,
- D ,upward,

**Q25: **

, , and are three points on one straight line, where , , and . Forces of magnitudes 2 N and 4 N are acting vertically downward at the two points and , respectively, and a force having a magnitude of 8 N is acting vertically upward at the point . Find the magnitude and direction of the resultant and the distance of its point of action from the point .

- A ,upward,
- B , downward,
- C , downward,
- D ,upward,