This is the Multiples Choice Questions Part 1 of the Series in Engineering Mechanics as one of the General Engineering and Applied Sciences (GEAS) topic. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including past Board Questions in General Engineering and Applied Sciences (GEAS) field.

### Online Questions and Answers in Engineering Mechanics Series

Following is the list of multiple choice questions in this brand new series:

**Engineering Mechanics MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

**MCQs from Number 51 – 100**Answer key:

**PART II**

**MCQs from Number 101 – 150**Answer key:

**PART III**

**MCQs from Number 151 – 200**Answer key:

**PART IV**

**MCQs from Number 201 – 250**Answer key:

**PART V**

**MCQs from Number 251 – 300**Answer key:

**PART VI**

**MCQs from Number 301 – 350**Answer key:

**PART VII**

**MCQs from Number 351 – 400**Answer key:

**PART VIII**

### Start Practice Exam Test Questions Part I of the Series

**Choose the letter of the best answer in each questions.**

1.What is the magnitude of the resultant force of the two forces which are perpendicular to each other? The two forces are 20 units and 30 units respectively.

- A. 36
- B. 42
- C. 25
- D. 40

2. A rope is stretched between two rigid walls 40 feet apart. At the midpoint, a load of 100 lbs was placed that caused it to sag 5 feet. Compute the approximate tension in the rope.

- A. 206 lbs
- B. 150 lbs
- C. 280 lbs
- D. 240 lbs

3. What is the effective component applied on the box that is being pulled by a 30 N force inclined at 30 degrees with horizontal?

- A. 36.21 N
- B. 25.98 N
- C. 15.32 N
- D. 20.62 N

4. A post is supported by a guy wire which exerts a pull of 100 N on the top of the post. If the angle between the wire and the ground is 60 degrees, what is the horizontal component of the force supporting the pole?

- A. 86.6 N
- B. 50.0 N
- C. 76.6 N
- D. 98.5 N

5. The resultant of two forces in a plane is 400 N at 120 degrees. If one of the forces is 200 lbs at 20 degrees what is the other force?

- A. 347.77 N at 114.85 degrees
- B. 435.77 N at 104.37 degrees
- C. 357.56 N at 114.24 degrees
- D. 477.27 N at 144.38 degrees

6. Determine the resultant of the following forces: A = 600 N at 40 degrees, B = 800 N at 160 degrees and C = 200 N at 300 degrees.

- A. 532.78 N, 55.32 degrees
- B. 435.94 N, 235.12 degrees
- C. 522.68 N, 111.57 degrees
- D. 627.89 N, 225.81 degrees

7. A collar, which may slide on a vertical rod is subjected three forces. Force A is 1200 N vertically upward, Force B is 800 N at an angle of 60 degrees from the vertical and a force F which is vertically downward to the right. Find the direction of F if its magnitude is 2400 N and the resultant is horizontal.

- A. 41.61 degrees
- B. 43.52 degrees
- C. 40.13 degrees
- D. 45.52 degrees

8. Given the 3-dimensional vectors: A = i(xy) + j(2yz) + k(3zx) and B = i(yz) + j(2zx) + k(3xy). Determine the scalar product at the point (1,2,3).

- A. 144
- B. 138
- C. 132
- D. 126

9. Determine the divergence of the vector: V = i(x2) + j(-xy) + k(xyz) at the point (3,2,1).

- A. 9.00
- B. 11.00
- C. 13.00
- D. 7.00

10.The three vectors described by 10 cm/ at 120k degrees, k = 0, 1, 2 encompass the sides of an equilateral triangle. Determine the magnitude of the vector cross product: 0.5 [ (10/ at 0 deg) x (10/ at 120 deg) ].

- A. 86.6
- B. 25.0
- C. 50.0
- D. 43.3

11. The 5 vectors: 10 cm/ at 72k degrees, k = 0, 1, 2, 3, 4 encompass the sides of a regular pentagon. Determine the magnitude of the vector cross product: 2.5 [ (10/ at 144 deg) x (10/ at 216 deg) ].

- A. 198.1
- B. 237.7
- C. 285.2
- D. 165.1

12. What is the angle between two vectors A and B if A = 4i – 12j + 6k and B = 24i – 8j + 6k?

- A. 168.45 degrees
- B. 84.32 degrees
- C. 86.32 degrees
- D. -84.64 degrees

13. Given the 3-dimensional vectors : A = i (xy) + j (2yz) + k (3zx), B = i (yz) + j (2zx) + k (3xy). Determine the magnitude of the vector sum |A + B| at coordinates (3,2,1).

- A. 32.92
- B. 29.88
- C. 27.20
- D. 24.73

14. What is the cross product A x B of the vectors, A = I + 4j + 6k and B = 2i + 3j + 5k ?

- A. i – j – k
- B. –i + j+ k
- C. 2i + 7j – 5k
- D. 2i + 7j + 5k

15. A simply supported beam is five meters in length. It carries a uniformly distributed load including its own weight of 300 N/m and a concentrated load of 100 N, 2 meters from the left end. Find the reactions if reaction A at the left end and reaction B at the right end.

- A. RA = 810 N, RB = 700 N
- B. RA = 820 N, RB = 690 N
- C. RA = 830 N, RB = 680 N
- D. RA = 840 N, RB = 670 N

16. A man can exert a maximum pull of 1,000 N but wishes to lift a new stone door for his cave weighing 20,000 N. If he uses a lever how much closer must the fulcrum be to the stone than to his hand?

- A. 10 times nearer
- B. 20 times farther
- C. 10 times farther
- D. 20 times nearer

17. A certain cable is suspended between two supports at the same elevation and 500 ft apart. The load is 500 lbs per horizontal foot including the weight of the cable. The sag of the cable is 30 ft. Calculate the total length of the cable.

- A. 503.21 ft
- B. 504.76 ft
- C. 505.12 ft
- D. 506.03 ft

18. The weight of a transmission cable is 1.5 kg/m distributed horizontally. If the maximum safe tension of the cable is 60000 kg and the allowable sag is 30 m, determine the horizontal distance between the electric posts supporting the transmission cable.

- A. 897 m
- B. 926 m
- C. 967 m
- D. 976 m

19. A cable 45.5 m long is carrying a uniformly distributed load along its span. If the cable is strung between two posts at the same level, 40 m apart, compute the smallest value that the cable may sag.

- A. 12.14 m
- B. 10.12 m
- C. 9.71 m
- D. 8.62 m

20.A pipeline crossing a river is suspended from a steel cable stretched between two posts 100 m apart. The weight of the pipe is 14 kg/m while the cable weighs 1 kg/m assumed to be uniformly distributed horizontally. If the allowed sag is 2 m, determine the tension of the cable at the post.

- A. 9047.28 kg
- B. 9404.95 kg
- C. 9545.88 kg
- D. 9245.37 kg

21. The distance between supports of a transmission cable is 20 m apart. The cable is loaded with a uniformly distributed load of 20 kN/m throughout its span. The maximum sag of the cable is 4 m. What is the maximum tension of the cable if one of the supports is 2 meters above the other?

- A. 415.53 N
- B. 413.43 N
- C. 427.33 N
- D. 414.13 N

22. A cable weighing 0.4 pound per foot and 800 feet long is to be suspended with sag of 80 feet. Determine the maximum tension of the cable.

- A. 403 kg
- B. 456 kg
- C. 416 kg
- D. 425 kg

23. A cable 200 m long weighs 50 N/m and is supported from two points at the same elevation. Determine the required sag if the maximum tension that the cable can carry shall not exceed 8000 N.

- A. 35.1 m
- B. 28.2 m
- C. 40.3 m
- D. 31.3 m

24. A transmission cable 300 m long, weighs 600 kg. The tensions at the ends of the cable are 400 kg and 450 kg. Find the distance of its lowest point to the ground.

- A. 145 m
- B. 148 m
- C. 150 m
- D. 153 m

25. A 250 kg block rests on a 30 degrees plane. If the coefficient of kinetic friction is 0.20, determine the horizontal force P applied on the block to start the block moving up the plane.

- A. 59.30 kg
- B. 58.10 kg
- C. 219.71 kg
- D. 265.29 kg

26. Compute the number of turns of the rope to be wound around a pole in order to support a man weighing 600 N with an input force of 10 N. Note: coefficient of friction is 0.30.

- A. 2.172
- B. 3.123
- C. 1.234
- D. 4.234

27. A block weighing 500 N is held by a rope that passes over a horizontal drum. The coefficient of friction between the rope and the drum is 0.15. If the angle of contact is 150 degrees, compute the force that will raise the object.

- A. 740.7 N
- B. 760.6 N
- C. 770.5 N
- D. 780.8 N

28. A cirlce has a diameter of 20 cm. Determine the moment of inertia of the circular area relative to the axis perpendicular to the area though the center of the circle in cm4.

- A. 14,280
- B. 15,708
- C. 17,279
- D. 19,007

29. What is the branch of engineering mechanics which refers to the study of stationary rigid body?

- A. Statics
- B. Kinetics
- C. Kinematics
- D. Dynamics

30. What is the branch of engineering mechanics which refers to the study of rigid body in motion under the action of forces?

- A. Statics
- B. Strenght of materials
- C. Kinematics
- D. Dynamics

31. What is the branch of engineering mechanics which refers to the study of rigid body in motion without reference to the force that causes the motion?

- A. Statics
- B. Kinetics
- C. Kinematics
- D. Dynamics

32. What refers to the force that holds part of the rigid body together?

- A. Natural force
- B. External force
- C. Internal force
- D. Concentrated force

33. What refers to a pair of equal, opposite and parallel forces?

- A. Couple
- B. Moment
- C. Torque
- D. All of the above

34. What is a concurrent force system?

- A. All forces act at the same point.
- B. All forces have the same line of action.
- C. All forces are parallel with one another.
- D. All forces are in the same plane.

35. When will a three-force member be considered in equilibrium?

- A. When the sum of the two forces is equal to the third force.
- B. When they are concurrent or parallel.
- C. When they are coplanar.
- D. All of the above

36. A roller support has how many reactions?

- A. None
- B. 1
- C. 2
- D. 3

37. A link or cable support has how many reactions?

- A. None
- B. 1
- C. 2
- D. 3

38. A build-in, fixed support has how many reactions and moment?

- A. 1 reaction and 1 moment
- B. 2 reactions and 1 moment
- C. 1 reaction and 2 moments
- D. 2 reactions and no moment

39. Which support has one moment?

- A. Frictionless guide
- B. Pin connection
- C. Fixed support
- D. Roller

40. What is the science that describes and predicts the effect on bodies at rest or in motion by forces acting on it?

- A. Engineering Mechanics
- B. Theory of Structures
- C. Mechanics of Materials
- D. Strength of Materials

41. What refers to a negligible body when compared to the distances involved regarding its motion?

- A. Particle
- B. Atomic substance
- C. Element
- D. Quarks

42. The resulting force of a distributed load is always acting at:

- A. the center of the beam subjected to the distributed load
- B. the centroid of the area of the loading curve
- C. the 1/3 point from the higher intensity side of the loading curve
- D. the 2/3 point from the higher intensity side of the loading curve

43. The resultant force of a distributed load is always equal to:

- A. twice the area under the loading curve
- B. half the area under the loading curve
- C. the area under the loading curve
- D. one-fourth the area under the loading curve

44. When a body has more supports than are necessary to maintain equilibrium, the body is said to be _____.

- A. in static equilibrium
- B. in dynamic equilibrium
- C. statically determine
- D. statically indeterminate

45. When does an equation be considered “dimensionally homogeneous”?

- A. When it is unitless
- B. When the dimensions of the various terms on the left side of the equation is not the same as the dimensions of the various terms on the right side.
- C. When the degree of the left side of the equation is the same as the right side.
- D. When the dimensions of various terms on the left side of the equation is the same as the dimensions of the various terms on the right side.

46. What refers to the branch of mathematics which deals with the dimensions of quantities?

- A. Unit analysis
- B. Dimensional analysis
- C. System analysis
- D. Homogeneity analysis

47. What is a “simple beam”?

- A. A beam supported only at its ends.
- B. A beam supported with a fixed support at one end and non on the other end.
- C. A beam with more than two supports.
- D. A beam with only one support at the midspan.

48. What assumption is used in the analysis of uniform flexible cable?

- A. Cable is flexible.
- B. Cable is inextensible.
- C. The weight of the cable is very small when compared to the loads supported by the cable.
- D. All of the above

49. “The sum of individual moments about a point caused by multiple concurrent forces is equal to the moment of the resultant force about the same point”. This statement is known as ____.

- A. Pappus proposition
- B. D’ Alembert’s principle
- C. Varignon’s theorem
- D. Newton’s method

50. “Two forces acting on a particle may be replaced by a single force called resultant which can be obtained by drawing diagonal of parallelogram, which has the sides equal to the given forces”. This statement is known as _____.

- A. Pappus Propositions
- B. Principle of Transmissibility
- C. Parallelogram Law
- D. Varignon’s Theorem

### Complete List of MCQs in General Engineering and Applied Science per topic

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