Engineering Mechanics 1000+ MCQ with answer for GATE

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

2. The potential energy of a vertically raised body is __________ the kinetic energy of a vertically falling body.
A. Equal to
B. Less than
C. Greater than
D. None of these
Answer : A

3. In a screw jack, the effort required to lift the load is given by (where W = Load lifted, ? = Helix angle, and ? = Angle of friction.)
A. P = W tan (? - ?)
B. P = W tan (? + ?)
C. P = W tan (? - ?)
D. P = W cos (? + ?)
Answer : B

4. The coefficient of restitution for inelastic bodies is
A. Zero
B. One
C. Between zero and one
D. More than one
Answer : A

5. The unit of work or energy in S.I. units is
A. Newton
B. Pascal
C. Watt
D. Joule
Answer : D

6. If three forces acting in different planes can be represented by a triangle, these will be in
A. Non-equilibrium
B. Partial equilibrium
C. Full equilibrium
D. Unpredictable
Answer : A

7. Forces are called coplanar when all of them acting on body lie in
A. One point
B. One plane
C. Different planes
D. Perpendicular planes
Answer : B

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

9. When a person, on a bicycle, drives round a curve, he has to lean __________ to maintain equilibrium.
A. Inward
B. Outward
C. Towards front
D. Towards back
Answer : A

10. The moment of inertia of a solid sphere of mass m and radius r is
A. 2mr²/3
B. 2mr²/5
C. mr²
D. mr²/2
Answer : B

11. 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

12. 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

13. If the resultant of two equal forces has the same magnitude as either of the forces, then the angle between the two forces is
A. 30°
B. 60°
C. 90°
D. 120°
Answer : D

14. 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

15. 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

16. The unit of angular velocity is
A. m/min
B. rad/s
C. Revolutions/min
D. Both (B) and (C)
Answer : D

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

18. The static friction
A. Bears a constant ratio to the normal reaction between the two surfaces
B. Is independent of the area of contact, between the two surfaces
C. Always acts in a direction, opposite to that in which the body tends to move
D. All of the above
Answer : D

19. The time of flight (t) of a projectile on an upward inclined plane is (where u = Velocity of projection, ? = Angle of projection, and ? = Inclination of the plane with the horizontal.)
A. t = g cos ?/2u sin (? - ?)
B. t = 2u sin (? - ?)/g cos ?
C. t = g cos ?/2u sin (? + ?)
D. t = 2u sin (? + ?)/g cos ?
Answer : B

20. 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

21. 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

strong>22. The angle which an inclined plane makes with the horizontal when a body placed on it is about to move down is known as angle of
A. Friction
B. Limiting friction
C. Repose
D. Kinematic friction
Answer : C

23. 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

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. 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

26. Concurrent forces are those forces whose lines of action
A. Lie on the same line
B. Meet at one point
C. Meet on the same plane
D. None of these
Answer : B

27. Which of the following statement is correct?
A. The kinetic energy of a body during impact remains constant.
B. The kinetic energy of a body before impact is equal to the kinetic energy of a body after impact.
C. The kinetic energy of a body before impact is less than the kinetic energy of a body after impact.
D. The kinetic energy of a body before impact is more than the kinetic energy of a body after impact.
Answer : D

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. Coplanar non-concurrent forces are those forces which __________ at one point, but their lines of action lie on the same plane.
A. Meet
B. Do not meet
C. Either A or B
D. None of these
Answer : B

30. Moment of inertia of a rectangular section having width (b) and depth (d) about an axis passing through its C.G. and parallel to the width (b), is
A. db³/12
B. bd³/12
C. db³/36
D. bd³/36
Answer : B

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

32. The length of a second's pendulum is
A. 94.9 cm
B. 99.4 cm
C. 100 cm
D. 101 cm
Answer : B

33. In order to completely specify angular displacement by a vector, it must fix
A. Direction of the axis of rotation
B. Magnitude of angular displacement
C. Sense of angular displacement
D. All of these
Answer : D

34. Pick up wrong statement about friction force for dry surfaces. Friction force is
A. Proportional to normal load between the surfaces
B. Dependent on the materials of contact surface
C. Proportional to velocity of sliding
D. Independent of the area of contact surfaces
Answer : C

35. An ideal machine is one whose efficiency is
A. Between 60 and 70 %
B. Between 70 and 80 %
C. Between 80 and 90 %
D. 100 %
Answer : D

36. The force, by which the body is attracted, towards the centre of the earth, is called
A. Impulsive force
B. Mass
C. Weight
D. Momentum
Answer : C

37. Least force required to draw a body up the inclined plane is W sin (plane inclination + friction angle) applied in the direction
A. Along the plane
B. Horizontally
C. Vertically
D. At an angle equal to the angle of friction to the inclined plane
Answer : D

38. The resultant of the following three couples 20 kg force, 0.5 m arm, +ve sense 30 kg force, 1 m arm, -ve sense 40 kg force, 0.25 m arm, +ve sense having arm of 0.5 m will be
A. 20 kg, -ve sense
B. 20 kg, + ve sense
C. 10 kg, + ve sense
D. 10 kg, -ve sense
Answer : A

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

41. Lami's theorem states that
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 actingat a point are in equilibrium, each force is proportional to the sine of the angle between the other two
Answer : D

42. The periodic time (T) is given by (where, ? = Angular velocity of particle in rad/s.)
A. ?/2?
B. 2?/?
C. 2? × ?
D. ?/?
Answer : B

43. The velocity of a body on reaching the ground from a height h, is
A. 2.?(gh)
B. ?(gh)
C. ?(2gh)
D. 2g.?h
Answer : C

44. 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

45. If a number of coplanar forces acting at a point be in equilibrium, the sum of clockwise moments must be __________ the sum of anticlockwise moments, about any point.
A. Equal to
B. Less than
C. Greater than
D. None of these
Answer : A

46. Which of the following is not the unit of work, energy and heat?
A. kcal
B. kg-m
C. kW-hr
D. h.p
Answer : D

47. Which of the following statement is correct?
A. The periodic time of a particle moving with simple harmonic motion is the time taken by a particle for one complete oscillation.
B. The periodic time of a particle moving with simple harmonic motion is directly proportional to its angular velocity.
C. The velocity of the particle moving with simple harmonic motion is zero at the mean position.
D. The acceleration of the particle moving with simple harmonic motion is maximum at the mean position.
Answer : A

48. The centre of gravity a T-section 100 mm × 150 mm × 50 mm from its bottom is
A. 50 mm
B. 75 mm
C. 87.5 mm
D. 125 mm
Answer : C

49. Mass moment of inertia of a uniform thin rod of mass M and length (l) about its mid-point and perpendicular to its length is
A. (2/3) Ml²
B. (1/3) Ml²
C. (3/4) Ml²
D. (1/12) Ml²
Answer : D

50. A pair of smith's tongs is an example of the lever of
A. Zeroth order
B. First order
C. Second order
D. Third order
Answer : C