Engineering Mechanics 1000+ MCQ with answer for JEE Main

1. 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

2. 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

3. Centre of gravity of a thin hollow cone lies on the axis at a height of
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 : B

4. 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

5. Coefficient 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 friction force acting when the body is just about to move
D. The friction force acting when the body is in motion
Answer : B

6. The periodic time of a particle with simple harmonic motion is __________ proportional to the angular velocity.
A. Directly
B. Inversely
C. Square root
D. None of these
Answer : B

7. 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

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

9. 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

10. The moment of inertia of a rectangular section 3 cm wide and 4 cm deep about X-X axis is
A. 9 cm⁴
B. 12 cm⁴
C. 16 cm⁴
D. 20 cm⁴
Answer : C

11. 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

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

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

14. Static friction is always __________ dynamic friction.
A. Equal to
B. Less than
C. Greater than
D. None of these
Answer : C

15. 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

16. 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

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

18. 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

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

20. According to the law of moments, 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 : C

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

22. The force required to move the body up the plane will be minimum if it makes an angle with the inclined plane __________ the angle of friction.
A. Equal to
B. Less than
C. Greater than
D. None of these
Answer : A

23. A screw jack used for lifting the loads is
A. A reversible machine
B. A non-reversible machine
C. An ideal machine
D. None of these
Answer : B

24. If u₁ and u₂ are the velocities of two moving bodies in the same direction before impact and v₁ and v₂ are their velocities after impact, then coefficient of restitution is given by
A. (v₁ - v₂)/(u₁ - u₂)
B. (v? - v?)/(u₁ - u₂)
C. (u₁ - u₂)/(v₁ - v₂)
D. (u? + u?)/(v? + v?)
Answer : B

25. 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

26. Tension in the cable supporting a lift is more when the lift is moving __________ with an acceleration.
A. Upwards
B. Downwards
C. Horizontal
D. None of these
Answer : A

27. The unit of moment of inertia of an area is
A. kg-m²
B. kg-m-s²
C. kg/m²
D. m⁴
Answer : D

28. 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

29. The efficiency of a screw jack is maximum, when (where ? = Helix angle, and ? = Angle of friction.)
A. ? = 45° + ?/2
B. ? = 45° - ?/2
C. ? = 90° + ?
D. ? = 90° - ?
Answer : B

30. Two blocks A and B of masses 150 kg and 50 kg respectively are connected by means of a string as shown in the below figure. The tension in all the three strings __________ be same.
A. Will
B. Will not
C. Either A or B
D. None of these
Answer : A

31. The force applied on a body of mass 100 kg to produce an acceleration of 5 m/s², is
A. 20 N
B. 100 N
C. 500 N
D. None of these
Answer : C

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

33. 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

34. 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

35. 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

36. 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

37. The unit of angular acceleration is
A. N-m
B. m/s
C. m/s2
D. rad/s2
Answer : D

38. If the body falls freely under gravity, then the gravitational acceleration is taken as
A. +8.9 m/s²
B. -8.9 m/s²
C. +9.8 m/s²
D. -9.8 m/s²
Answer : C

39. 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

40. 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

41. If n = number of members and y = number of joints, then for a perfect frame, n = ?
A. 1/2
B. 2/3
C. 3/2
D. 2/4
Answer : B

42. If a given force (or a given system of forces) acting on a body __________ the position of the body, but keeps it in equilibrium, then its effect is to produce internal stress in the body.
A. Change
B. Does not change
C Changes periodically
D. None of these
Answer : B

43. 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

44. Tangent of angle of friction is equal to
A. Kinetic friction
B. Limiting friction
C. Angle of repose
D. Coefficient of friction
Answer : D

45. Which is the correct statement about law of polygon of forces?
A. If any number of forces acting at a point can be represented by the sides of a polygon taken in order, then the forces are in equilibrium
B. If any number of forces acting at a point can be represented in direction and magnitude by the sides of a polygon, then the forces are in equilibrium
C. If a polygon representing forces acting at a point is closed then forces are in equilibrium
D. If any number of forces acting at a point can be represented in direction and magnitude by the sides of a polygon taken in order, then the forces are in equilibrium
Answer : D

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

49. 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

50. The periodic time of one oscillation for a simple pendulum is (where l = Length of the pendulum.)
A. (1/2?). ?(l/g)
B. (1/2?). ?(g/l)
C. 2?. ?(l/g)
D. None of these
Answer : C