Engineering Mechanics 1000+ MCQ with answer for UPSC CDS

1. A lead ball with a certain velocity is made to strike a wall, it falls down, but rubber ball of same mass and with same velocity strikes the same wall, it rebounds. Select the correct reason from the following:
A. Both the balls undergo an equal change in momentum
B. The change in momentum suffered by rubber ball is more than the lead ball
C. The change in momentum suffered by rubber ball is less than the lead ball
D. None of the above
Answer : B

2. The velocity ratio of a first system of pulleys with 4 pulleys is
A. 4
B. 8
C. 16
D. 20
Answer : C

3. 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

4. The C.G. of a solid hemisphere lies on the central radius 3r
A. At distance from the plane base 3r
B. At distance from the plane base 3r
C. At distance from the plane base 3r
D. At distance from the plane base
Answer : D

5. In the shown figure, if the angle of inclination of the plane is increased, then acceleration of the system will
A. Increase
B. Decrease
C. Remain the same
D. None of these
Answer : B

6. 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

7. One joule means that
A. Work is done by a force of 1 N when it displaces a body through 1 m
B. Work is done by a force of 1 kg when it displaces a body through 1 m
C. Work is done by a force of 1 dyne when it displaces a body through 1 cm
D. Work is done by a force of 1 g when it displaces a body through 1 cm
Answer : A

8. Two bodies of masses m1 and m2 are hung from the ends of a rope, passing over a frictionless pulley as shown in the figure below. The acceleration of the string will be
A. g (m₁ - m₂)/(m₁ + m₂)
B. 2g (m₁ - m₂)/(m₁ + m₂)
C. g (m₁ + m₂)/(m₁ - m₂)
D. 2g (m₁ + m₂)/(m₁ - m₂)
Answer : A

9. Centre of gravity of a solid cone lies on the axis at the height
A. One fourth of the total height above base
B. One third of the total height above base
C. One-half of the total height above base
D. Three eighth of the total height above the base
Answer : A

10. According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through centre of gravity (i.e. I_P) is given by(where, A = Area of the section, I_G = Moment of inertia of the section about an axis passing through its C.G., and h = Distance between C.G. and the parallel axis.)
A. I_P = I_G + Ah²
B. I_P = I_G - Ah²
C. I_P = I_G / Ah²
D. I_P = Ah² / I_G
Answer : A

11. The acceleration of a particle moving with simple harmonic motion, at any instant is given by
A. ?.y
B. ?².y
C. ?²/y
D. ?³.y
Answer : B

12. 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

13. 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

14. Which of the following is not a scalar quantity?
A. Mass
B. Volume
C. Density
D. Acceleration
Answer : D

15. Which of the following is an equation of linear motion? (where, u and v = Initial and final velocity of the body, a = Acceleration of the body, and s = Displacement of the body in time t seconds.)
A. v = u + a.t
B. s = u.t + ½ a.t²
C. v² = u² + 2a.s
D. All of these
Answer : D

16. 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

17. If the masses of both the bodies, as shown in the below figure, are reduced to 50 percent, then tension in the string will be
A. Same
B. Half
C. Double
D. None of these
Answer : B

18. The motion of a particle round a fixed axis is A. Translatory
B. Rotary
C. Circular
D. Translatory as well as rotary
Answer : C

19. 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

20. 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

21. 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

22. A spherical body is symmetrical about its perpendicular axis. According to Routh's rule, the moment of inertia of a body about an axis passing through its centre of gravity is (where, M = Mass of the body, and S = Sum of the squares of the two semi-axes.)
A. MS/3
B. MS/4
C. MS/5
D. None of these
Answer : C

23. The friction experienced by a body, when in motion, is known as
A. Rolling friction
B. Dynamic friction
C. Limiting friction
D. Static friction
Answer : B

24. Moment of inertia of a triangular section of base (b) and height (h) about an axis passing through its C.G. and parallel to the base, is
A. bh³/4
B. bh³/8
C. bh³/12
D. bh³/36
Answer : D

25. Angle of friction is the
A. Angle between normal reaction and the resultant of normal reaction and the limiting friction
B. Ratio of limiting friction and normal reaction
C. The ratio of minimum friction force to the friction force acting when the body is just about to move
D. The ratio of minimum friction force to friction force acting when the body is in motion
Answer : A

26. The centre of gravity of a uniform lamina lies at
A. The centre of heavy portion
B. The bottom surface
C. The midpoint of its axis
D. All of the above
Answer : C

27. The maximum frictional force which comes into play when a body just begins to slide over another surface is called
A. Limiting friction
B. Sliding friction
C. Rolling friction
D. Kinematic friction
Answer : A

28. The term 'Centroid' is
A. The same as centre of gravity
B. The point of suspension
C. The point of application of the resultant of all the forces tending to cause a body to rotate about a certain axis
D. None of the above
Answer : A

29. The frequency of oscillation of a compound pendulum is (where kG = Radius of gyration about the centroidal axis, and h = Distance between the point of suspension and C.G. of the body.)
A. 2?. ?(gh/kG² + h²)
B. 2?. ?(kG² + h²/gh)
C. 1/2?. ?(gh/kG² + h²)
D. 1/2?. ?(kG² + h²/gh)
Answer : C

30. 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

31. Dynamic friction as compared to static friction is
A. Same
B. More
C. Less
D. May be less of more depending on nature of surfaces and velocity
Answer : C

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. The maximum mechanical advantage of a lifting machine is
A. 1 + m
B. 1 - m
C. 1 / m
D. m
Answer : C

40. 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

41. The ratio of static friction to dynamic friction is always
A. Equal to one
B. Less than one
C. Greater than one
D. None of these
Answer : C

42. 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

43. Pick up the incorrect statement from the following:
A. The C.G. of a circle is at its centre
B. The C.G. of a triangle is at the intersection of its medians
C. The C.G. of a rectangle is at the intersection of its diagonals
D. The C.G. of a semicircle is at a distance of r/2 from the centre
Answer : D

44. One watt is equal to
A. 0.1 joule/s
B. 1 joule/s
C. 10 joules/s
D. 100 joules/s
Answer : B

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 framed structure is perfect if it contains members equal to
A. 2n³
B. 2n
C. n²
D. 3n² Where n = number of joints in a frame
Answer : A

47. A circular hole of 50 mm diameter is cut out from a circular disc of 100 mm diameter as shown in the below figure. The centre of gravity of the section will lie
A. In the shaded area
B. In the hole
C. At O
D. None of these
Answer : A

48. If a suspended body is struck at the centre of percussion, then the pressure on die axis passing through the point of suspension will be
A. Maximum
B. Minimum
C. Zero
D. Infinity
Answer : C

49. The acceleration of a body sliding down an inclined surface is
A. g sin?
B. g cos?
C. g tan?
D. None of these
Answer : A

50. A heavy ladder resting on floor and against a vertical wall may not be in equilibrium, if
A. The floor is smooth, the wall is rough
B. The floor is rough, the wall is smooth
C. The floor and wall both are smooth surfaces
D. The floor and wall both are rough surfaces
Answer : C