Engineering Mechanics 1000+ MCQ with answer for CAT

1. When two elastic bodies collide with each other,
A. The two bodies will momentarily come to rest after collision
B. The two bodies tend to compress and deform at the surface of contact
C. The two bodies begin to regain their original shape
D. All of the above
Answer : D

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

3. The bellow figure shows the three coplanar forces P, Q and R acting at a point O. If these forces are in equilibrium, then
A. P/sin ? = Q/sin ? = R/sin ?
B. P/sin ? = Q/sin ? = R/sin ?
C. P/sin ? = Q/sin ? = R/sin ?
D. P/sin ? = Q/sin ? = R/sin ?
Answer : B

4. 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

5. The velocity of a particle (v) moving with simple harmonic motion, at any instant is given by (where r = Amplitude of motion, and y = Displacement of the particle from mean position.)
A. ?.?(y² - r²)
B. ?.?(r² - y²)
C. ?².?(y² - r²)
D. ?².?(r² - y²)
Answer : B

6. 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

7. If P is the force acting on the body, m is the mass of the body and a is the acceleration of the body, then according to Newton's second law of motion,
A. P + m.a = 0
B. P - m.a = 0
C. P × m.a = 0
D. P/m.a = 0
Answer : B

8. A machine having an efficiency greater than 50%, is known as
A. Reversible machine
B. Non-reversible machine
C. Neither reversible nor non-reversible machine
D. Ideal machine
Answer : A

9. In the lever of third order, load W, effort P and fulcrum F are oriented as follows
A. W between P and F
B. F between W and P
C. P between W and F
D. W, P and F all on one side
Answer : A

10. A pendulum which executes one beat per second is known as
A. Simple pendulum
B. Compound pendulum
C. Torsional pendulum
D. Second's pendulum
Answer : D

11. The centre of gravity of a triangle lies at the point of
A. Concurrence of the medians
B. Intersection of its altitudes
C. Intersection of bisector of angles
D. Intersection of diagonals
Answer : A

12. 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

13. The centre of gravity of a right circular solid cone is at a distance of __________ from its base, measured along the vertical axis. (where h = Height of a right circular solid cone.)
A. h/2
B. h/3
C. h/4
D. h/6
Answer : C

14. Kinetic friction is the
A. Tangent of angle between normal reaction and the resultant of normal reaction and the 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 : D

15. 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

16. The horizontal range of a projectile (R) is given by
A. R = u² cos2?/g
B. R = u² sin2?/g
C. R = u² cos?/g
D. R = u² sin?/g
Answer : B

17. The forces, whose lines of action are parallel to each other and act in the same directions, are known as
A. Coplanar concurrent forces
B. Coplanar non-concurrent forces
C. Like parallel forces
D. Unlike parallel forces
Answer : C

18. A weight of 1000 N can be lifted by an effort of 80 N. If the velocity ratio is 20, the machine is
A. Reversible
B. Non-reversible
C. Ideal
D. None of these
Answer : A

19. The wheels of a moving car possess
A. Potential eergy only
B. Kinetic energy of translation only
C. Kinetic energy of rotation only
D. Kinetic energy of translation and rotation both
Answer : D

20. 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

21. In a framed structure, as shown in the below figure, the force in the member BC is
A. W/?3 (compression)
B. W/?3 (tension)
C. 2W/?3 (compression)
D. 2W/?3 (tension)
Answer : D

22. The moment of inertia of a thin rod of mass m and length l, about an axis through its centre of gravity and perpendicular to its length is
A. ml²/4
B. ml²/ 6
C. ml²/8
D. ml²/12
Answer : D

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

24. 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

25. The range of projectile (R) on an upward inclined plane is
A. g. cos² ?/2u². sin (? + ?). cos ?
B. 2u². sin (? + ?). cos ?/g. cos² ?
C. g. cos² ?/2u². sin (? - ?). cos ?
D. 2u². sin (? - ?). cos ?/g. cos² ?
Answer : D

26. 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

27. Which of the following is the locus of a point that moves in such a manner that its distance from a fixed point is equal to its distance from a fixed line multiplied by a constant greater than one
A. Ellipse
B. Hyperbola
C. Parabola
D. Circle
Answer : B

28. 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

29. 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

30. 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

31. 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

32. The range of a projectile is maximum, when the angle of projection is
A. 30°
B. 45°
C. 60°
D. 90°
Answer : B

33. Moment of inertia of a hollow circular section, as shown in the below figure about X-axis, is
A. ?/16 (D² - d²)
B. ?/16 (D³ - d³)
C. ?/32 (D? - d?)
D. ?/64 (D? - d?)
Answer : D

34. A machine having an efficiency less than 50%, is known as
A. Reversible machine
B. Non-reversible machine
C. Neither reversible nor non-reversible machine
D. Ideal machine
Answer : B

35. The process of finding out the resultant force is called __________ of forces.
A. Composition
B. Resolution
C. Decomposition
D. None of these
Answer : A

36. The velocity of a particle moving with simple harmonic motion is __________ at the mean position.
A. Zero
B. Minimum
C. Maximum
D. None of these
Answer : C

37. The impact between two lead spheres is approximately equal to an __________ impact.
A. Elastic
B. Inelastic
C. Solid
D. None of these
Answer : B

38. The moment of inertia of a sphere of mass m and radius r, about an axis tangential to it, is
A. 2mr²/3
B. 2mr²/5
C. 7mr²/3
D. 7mr²/5
Answer : D

39. If three forces acting in one plane upon a rigid body, keep it in equilibrium, then they must either
A. Meet in a point
B. Be all parallel
C. At least two of them must meet
D. All the above are correct
Answer : D

40. The rate of change of momentum is directly proportional to the impressed force, and takes place in thesame direction in which the force acts. This statement is known as
A. Newton's first law of motion
B. Newton's second law of motion
C. Newton's third law of motion
D. None of these
Answer : B

41. A differential pulley block has larger and smaller diameters of 100 mm and 80 mm respectively. Its velocity ratio is
A. 5
B. 10
C. 20
D. 40
Answer : B

42. The minimum force required to slide a body of weight W on a rough horizontal plane is
A. W sin?
B. W cos?
C. W tan?
D. None of these
Answer : C

43. 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

44. 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

45. 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 acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two
Answer : D

46. 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

47. If a body is acted upon by a number of coplanar non-concurrent forces, it may
A. Rotate about itself without moving
B. Move in any one direction rotating about itself
C. Be completely at rest
D. All of these
Answer : D

48. 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 depth (d), is
A. db³/12
B. bd³/12
C. db³/36
D. bd³/36
Answer : A

49. When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as
A. Simple pendulum
B. Compound pendulum
C. Torsional pendulum
D. Second's pendulum
Answer : B

50. 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