1000+ Engineering Mechanics MCQ for GRE [Solved]

1. Varingon's theorem of moments states that if a number of coplanar forces acting on a particle are in equilibrium, then
A. Their algebraic sum is zero
B. Their lines of action are at equal distances
C. The algebraic sum of their moments about any point in their plane is zero
D. The algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point.
Answer : D

2. The force induced in the string AB due to the load W, as shown in the below figure is
A. W sin?
B. W cos?
C. W sec?
D. W cosec?
Answer : D

3. The maximum velocity of a particle moving with simple harmonic motion is
A. ?
B. ?r
C. ?²r
D. ?/r
Answer : B

4. A force while acting on a body may
A. Change its motion
B. Balance the forces, already acting on it
C. Give rise to the internal stresses in it
D. All of these
Answer : D

5. In a single threaded worm and worm wheel, the number of teeth on the worm is 50. The diameter of the effort wheel is 100 mm and that of load drum is 50 mm. The velocity ratio is
A. 50
B. 100
C. 200
D. 400
Answer : B

6. The unit of force in S.I. units is
A. kilogram
B. Newton
C. Watt
D. Dyne
Answer : B

7. The skidding away of the vehicle on a level circular path can be avoided if the force of friction between the wheels and the ground is __________ the centrifugal force.
A. Less than
B. Greater than
C. Equal to
D. None of these
Answer : B

8. Two like parallel forces are acting at a distance of 24 mm apart and their resultant is 20 N. It the line of action of the resultant is 6 mm from any given force, the two forces are
A. 15 N and 5 N
B. 20 N and 5 N
C. 15 N and 15 N
D. None of these
Answer : A

9. The velocity ratio for the third system of pulleys is
A. n
B. n²
C. 2n
D. 2n - 1
Answer : D

10. The weight of a body is due to
A. Gravitational pull exerted by the earth
B. Forces experienced by body in atmosphere
C. Force of attraction experienced by particles
D. Gravitational force of attraction towards the centre of the earth
Answer : D

11. Frictional force encountered after commencement of motion is called
A. Limiting friction
B. Kinematic friction
C. Frictional resistance
D. Dynamic friction
Answer : D

12. A single force and a couple acting in the same plane upon a rigid body
A. Balance each other
B. Cannot balance each other
C. Produce moment of a couple
D. Are equivalent
Answer : B

13. Which of the following statement is incorrect?
A. A force acting in the opposite direction to the motion of the body is called force of friction
B. The ratio of the limiting friction to the normal reaction is called coefficient of friction
C. A machine whose efficiency is 100% is known as an ideal machine
D. The velocity ratio of a machine is the ratio of load lifted to the effort applied
Answer : D

14. Two forces are acting at an angle of 120°. The bigger force is 40 N and the resultant is perpendicular to the smaller one. The smaller force is
A. 20 N
B. 40 N
C. 120 N
D. None of these
Answer : A

15. A force is completely defined when we specify
A. Magnitude
B. Direction
C. Point of application
D. All of the above
Answer : D

16. The velocity ratio in case of an inclined plane inclined at angle ? to the horizontal and weight being pulled up the inclined plane by vertical effort is
A. sin?
B. cos?
C. tan?
D. cosec?
Answer : A

17. The Cartesian equation of trajectory is (where u = Velocity of projection, ? = Angle of projection, and x, y = Co-ordinates of any point on the trajectory after t seconds.)
A. y = (gx²/2u² cos²?) + x. tan?
B. y = (gx²/2u² cos²?) - x. tan?
C. y = x. tan? - (gx²/2u² cos²?)
D. y = x. tan? + (gx²/2u² cos²?)
Answer : C

18. The maximum frictional force, which comes into play, when a body just begins to slide over the surface of the other body, is known as
A. Static friction
B. Dynamic friction
C. Limiting friction
D. Coefficient of friction
Answer : C

19. Three forces acting on a rigid body are represented in magnitude, direction and line of action by the three sides of a triangle taken in order. The forces are equivalent to a couple whose moment is equal to
A. Area of the triangle
B. Twice the area of the triangle
C. Half the area of the triangle
D. None of these
Answer : B

20. The principle of transmissibility of forces states that, when a force acts upon a body, its effect is
A. Same at every point on its line of action
B. Different at different points on its line of action
C. Minimum, if it acts at the centre of gravity of the body
D. Maximum, if it acts at the centre of gravity of the body
Answer : C

21. The units of moment of inertia of an area are
A. kg-m²
B. m?
C. kg/m²
D. m³
Answer : B

22. One kg force is equal to
A. 7.8 N
B. 8.9 N
C. 9.8 N
D. 12 N
Answer : C

23. The forces which do not meet at one point and their lines of action do not lie on the same plane are known as
A. Coplanar concurrent forces
B. Coplanar non-concurrent forces
C. Non-coplanar concurrent forces
D. None of these
Answer : D

24. Coplanar concurrent forces are those forces which
A. Meet at one point, but their lines of action do not lie on the same plane
B. Do not meet at one point and their lines of action do not lie on the same plane
C. Meet at one point and their lines of action also lie on the same plane
D. Do not meet at one point, but their lines of action lie on the same plane
Answer : C

25. A projectile is fired at an angle ? to the vertical. Its horizontal range will be maximum when ? is
A. 0°
B. 30°
C. 45°
D. 60°
Answer : C

26. During elastic impact, the relative velocity of the two bodies after impact is __________ the relative velocity of the two bodies before impact.
A. Equal to
B. Equal and opposite to
C. Less than
D. Greater than
Answer : B

27. The M.I. of hollow circular section about a central axis perpendicular to section as compared to its M.I. about horizontal axis is
A. Same
B. Double
C. Half
D. Four times
Answer : B

28. The total momentum of a system of masses (i. e. moving bodies) in any one direction remains constant, unless acted upon by an external force in that direction. This statement is called
A. Newton's first law of motion
B. Newton's second law of motion
C. Principle of conservation of energy
D. Principle of conservation of momentum
Answer : D

29. Moment of inertia of a circular section about an axis perpendicular to the section is
A. ?d³/16
B. ?d³/32
C. ?d⁴/32
D. ?d⁴/64
Answer : C

30. The three forces of 100 N, 200 N and 300 N have their lines of action parallel to each other but act in the opposite directions. These forces are known as
A. Coplanar concurrent forces
B. Coplanar non-concurrent forces
C. Like parallel forces
D. Unlike parallel forces
Answer : D

31. Which of the following is not the unit of energy?
A. kg m
B. kcal
C. Watt
D. Watt hours
Answer : C

32. Which of the following do not have identical dimensions?
A. Momentum and impulse
B. Torque and energy
C. Torque and work
D. Moment of a force and angular momentum.
Answer : D

33. Moment of inertia is the
A. Second moment of force
B. Second moment of area
C. Second moment of mass
D. All of these
Answer : D

34. A smooth cylinder lying on a __________ is in neutral equilibrium.
A. Curved surface
B. Convex surface
C. Horizontal surface
D. None of these
Answer : C

35. A body moves, from rest with a constant acceleration of 5 m per sec. The distance covered in 5 sec is most nearly
A. 38 m
B. 62.5 m
C. 96 m
D. 124 m
Answer : B

36. The ideal angle of banking provided on the curves on roads depends upon
A. Weight of the vehicle
B. (Velocity)2 of the vehicle
C. Nature of the road surface
D. Coefficient of friction between the road and vehicle contact point
Answer : B

37. Which of the following statement is correct?
A. The algebraic sum of the forces, constituting the couple is zero
B. The algebraic sum of the forces, constituting the couple, about any point is the same
C. A couple cannot be balanced by a single force but can be balanced only by a couple of opposite sense
D. All of the above
Answer : D

38. If a number of forces are acting at a point, their resultant will be inclined at an angle ? with the horizontal, such that
A. tan? = ?H/?V
B. tan? = ?V/?H
C. tan? = ?V × ?H
D. tan? = ?(?V + ?H)
Answer : B

39. The time of flight of a projectile on downward inclined plane depends upon
A. Angle of projection
B. Angle of inclination of the plane
C. Both (A) and (B)
D. None of these
Answer : C

40. The forces which meet at one point, but their lines of action __________ on the same plane, are Known as non-coplanar concurrent forces.
A. Lie
B. Do not lie
C. Either A or B
D. None of these
Answer : B

41. In order to double the period of simple pendulum, the length of the string should be
A. Halved
B. Doubled
C. Quadrupled
D. None of these
Answer : C

42. The loss of kinetic energy during inelastic impact, is given by (where m₁ = Mass of the first body, m₂ = Mass of the second body, and u₁ and u₂ = Velocities of the first and second bodies respectively.)
A. [m? m?/2(m? + m?)] (u? - u?)²
B. [2(m? + m?)/m? m?] (u? - u?)²
C. [m? m?/2(m? + m?)] (u?² - u?²)
D. [2(m? + m?)/m? m?] (u?² - u?²)
Answer : A

43. Work done is said to be zero, when
A. Some force acts on a body, but displacement is zero
B. No force acts on a body but some displacement takes place
C. Either (A) or (B)
D. None of the above
Answer : C

44. The friction experienced by a body, when at rest, is known as
A. Static friction
B. Dynamic friction
C. Limiting friction
D. Coefficient of friction
Answer : A

45. The resultant of two forces P and Q acting at an angle ? is
A. ?(P² + Q² + 2PQ sin?)
B. ?(P² + Q² + 2PQ cos?)
C. ?(P² + Q² - 2PQ cos?)
D. ?(P² + Q² - 2PQ tan?)
Answer : B

46. For any system of coplanar forces, the condition of equilibrium is that the
A. Algebraic sum of the horizontal components of all the forces should be zero
B. Algebraic sum of the vertical components of all the forces should be zero
C. Algebraic sum of moments of all the forces about any point should be zero
D. All of the above
Answer : D

47. The coefficient of friction depends upon
A. Nature of surfaces
B. Area of contact
C. Shape of the surfaces
D. All of the above
Answer : A

48. The angular velocity (in rad/s) of a body rotating at N revolutions per minute is
A. ?N/60
B. ?N/180
C. 2?N/60
D. 2?N/180
Answer : C

49. A redundant frame is also called __________ frame.
A. Perfect
B. Imperfect
C. Deficient
D. None of these
Answer : B

50. The rate of change of displacement of a body is called
A. Velocity
B. Acceleration
C. Momentum
D. None of these
Answer : A