Engineering Mechanics 1000+ MCQ with answer for UPSC IES

1. If a rigid body is in equilibrium under the action of three forces, then
A. These forces are equal
B. The lines of action of these forces meet in a point
C. The lines of action of these forces are parallel
D. Both (B) and (C) above
Answer : D

2. The moment of the force P about O as shown in the below figure is
A. P × OA
B. P × OB
C. P × OC
D. P × AC
Answer : C

3. 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

4. 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

5. Which of the following is not the unit of power?
A. kW (kilowatt)
B. hp (horse power)
C. kcal/sec
D. kcal/kg sec
Answer : D

6. The resultant of the two forces P and Q is R. If Q is doubled, the new resultant is perpendicular to P. Then
A. P = Q
B. Q = R
C. Q = 2R
D. None of these
Answer : B

7. The rate of doing work is known as
A. Potential energy
B. Kinetic energy
C. Power
D. None of these
Answer : C

8. 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

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

10. Limiting force of friction is the
A. Tangent of angle between normal reaction and the resultant of normal reaction and limiting friction
B. Ratio of limiting friction and normal reaction
C. The friction force acting when the body is just about to move
D. The friction force acting when the body is in motion
Answer : C

11. The moment of inertia of a square of side a about its diagonal is
A. a²/8
B. a³/12
C. a⁴/12
D. a⁴/16
Answer : C

12. According to principle of moments
A. If a system of coplanar forces is in equilibrium, then their algebraic sum is zero
B. If a system of coplanar forces is in equilibrium, then the algebraic sum of their moments about any point in their plane is zero
C. The algebraic sum of the moments of any two forces about any point is equal to moment of the resultant about the same point
D. Positive and negative couples can be balanced
Answer : B

13. A ladder is resting on a smooth ground and leaning against a rough vertical wall. The force of friction will act
A. Towards the wall at its upper end
B. Away from the wall at its upper end
C. Downward at its upper end
D. Upward at its upper end
Answer : D

14. Coulomb friction is the friction between
A. Bodies having relative motion
B. Two dry surfaces
C. Two lubricated surfaces
D. Solids and liquids
Answer : A

15. One end of a helical spring is fixed while the other end carries the load W which moves with simple harmonic motion. The frequency of motion is given by (where ? = Deflection of the spring.)
A. 2?. ?(g/?)
B. 1/2?. ?(g/?)
C. 2?. ?(?/g)
D. 1/2?. ?(?/g)
Answer : B

16. 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

17. A body will begin to move down an inclined plane if the angle of inclination of the plane is _________ the angle of friction.
A. Equal to
B. Less than
C. Greater than
D. None of these
Answer : C

18. The mechanical advantage of a lifting machine is the ratio of
A. Distance moved by effort to the distance moved by load
B. Load lifted to the effort applied
C. Output to the input
D. All of the above
Answer : B

19. Which of the following are vector quantities?
A. Angular displacement
B. Angular velocity
C. Angular acceleration
D. All of these
Answer : D

20. If a number of forces act simultaneously on a particle, it is possible
A. Not a replace them by a single force
B. To replace them by a single force
C. To replace them by a single force through C.G.
D. To replace them by a couple
Answer : B

21. If tension in the cable supporting a lift moving downwards is half the tension when it is moing upwards, the acceleration of the lift is
A. g/2
B. g/3
C. g/4
D. None of these
Answer : D

22. A smooth cylinder lying on its convex surface remains in __________ equilibrium.
A. Stable
B. Unstable
C. Neutral
D. None of these
Answer : B

23. In the shown figure, the tension (T) in the string will be
A. m?. m?. g/(m? + m?)
B. 2m?. m?. g/(m? + m?)
C. (m? + m?)/ m?. m?. g
D. (m? + m?)/2m?. m?. g
Answer : B

24. Joule is the unit of
A. Force
B. Work
C. Power
D. Velocity
Answer : B

25. The range of projectile on a downward inclined plane is ________ the range on upward inclined plane for the same velocity of projection and angle of projection.
A. Less than
B. More than
C. Equal to
D. None of These
Answer : B

26. The efficiency of a lifting machine is the ratio of
A. Output to the input
B. Work done by the machine to the work done on the machine
C. Mechanical advantage to the velocity ratio
D. All of the above
Answer : D

27. If a number of forces are acting at a point, their resultant is given by
A. (?V)² + (?H)²
B. ?[(?V)² + (?H)²]
C. (?V)² +(?H)² +2(?V)(?H)
D. ?[(?V)² +(?H)² +2(?V)(?H)]
Answer : B

28. If the masses of both the bodies, as shown in the below figure, are doubled, then the acceleration in the string will be
A. Same
B. Half
C. Double
D. None of these
Answer : A

29. 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

30. The unit of power in S.I. units is
A. Horsepower
B. Joule
C. Watt
D. kg-m
Answer : C

31. The coefficient of friction depends on
A. Area of contact
B. Shape of surfaces
C. Strength of surfaces
D. Nature of surface
Answer : D

32. The point, through which the whole weight of the body acts, irrespective of its position, is known as
A. Moment of inertia
B. Centre of gravity
C. Centre of percussion
D. Centre of mass
Answer : B

33. Non-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 : A

34. Moment of inertia of a circular section about its diameter (d) is
A. ?d³/16
B. ?d³/32
C. ?d⁴/32
D. ?d⁴/64
Answer : D

35. A framed structure is perfect, if the number of members are __________ (2j - 3), where j is the number of joints.
A. Equal to
B. Less than
C. Greater than
D. None of these
Answer : A

36. The centre of percussion is below the centre of gravity of the body and is at a distance equal to
A. h/kG
B. h²/kG
C. kG²/h
D. h × kG
Answer : C

37. The C.G. of a plane lamina will not be at its geometrical centre in the case of a
A. Right angled triangle
B. Equilateral triangle
C. Square
D. Circle
Answer : A

38. According to law of triangle of forces
A. Three forces acting at a point will be in equilibrium
B. Three forces acting at a point can be represented by a triangle, each side being proportional to force
C. If three forces acting upon a particle are represented in magnitude and direction by the sides of a triangle, taken in order, they will be in equilibrium
D. If three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two
Answer : C

39. A body of mass m moving with a constant velocity v strikes another body of same mass moving with same velocity but in opposite direction. The common velocity of both the bodies after collision is
A. v
B. 2v
C. 4v
D. 8v
Answer : B

40. Two non-collinear parallel equal forces acting in opposite direction
A. Balance each other
B. Constitute a moment
C. Constitute a couple
D. Constitute a moment of couple
Answer : C

41. The resultant of two equal forces P making an angle ?, is given by
A. 2P sin?/2
B. 2P cos?/2
C. 2P tan?/2
D. 2P cot?/2
Answer : B

42. The centre of percussion of the homogeneous rod of length L suspended t the top will be
A. L/2
B. L/3
C. 3L/4
D. 2L/3
Answer : D

43. The maximum height of a projectile on a horizontal plane, is
A. u² sin²?/2g
B. u² cos²?/2g
C. u² sin²?/g
D. u² cos²?/g
Answer : A

44. A number of forces acting at a point will be in equilibrium, if
A. All the forces are equally inclined
B. Sum of all the forces is zero
C. Sum of resolved parts in the vertical direction is zero (i.e. ?V = 0)
D. None of these
Answer : C

45. A force acting on a body may
A. Change its motion
B. Balance the other forces acting on it
C. Retard its motion
D. All of the above
Answer : D

46. A block of mass 20 kg lying on a rough horizontal plane is connected by a light string passing over a smooth pulley to another mass 5 kg, which can move freely in the Vertical direction, as shown in the below figure. The tension in the string will __________ with the increase in coefficient of friction.
A. Increase
B. Decrease
C. Not be effected
D. None of these
Answer : A

47. A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is ?. The effort applied parallel to the plane is given by (where ? = tan? = Coefficient of friction between the plane and the body.)
A. P = W tan?
B. P = W tan (? + ?)
C. P = W (sin? + ?cos?)
D. P = W (cos? + ?sin?)
Answer : C

48. 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

49. A heavy string attached at two ends at same horizontal level and when central dip is very small approaches the following curve
A. Circular arc
B. Parabola
C. Hyperbola
D. Elliptical
Answer : B

50. If the number of pulleys in a system is equal to its velocity ratio, then it is a __________ system of pulleys
A. First
B. Second
C. Third
D. None of these
Answer : B