Engineering Mechanics – Section 3: Fundamentals, Force Systems, Equilibrium & MCQs
Engineering Mechanics – Section 3: Fundamentals, Force Systems, Equilibrium & MCQs is a comprehensive learning resource designed to help engineering students build a strong foundation in the core principles of engineering mechanics. This section covers essential topics including the fundamentals of mechanics, force systems, vector representation of forces, resultant and resolution of forces, moments, couples, equilibrium conditions, free body diagrams (FBD), and practical engineering applications.
The study material is presented in a clear and structured manner, making it suitable for diploma, B.Tech, BE, polytechnic, and competitive examination aspirants. Along with detailed theoretical explanations, this section includes carefully selected multiple-choice questions (MCQs) with answers to strengthen conceptual understanding and improve problem-solving skills.
Whether you are preparing for semester examinations, engineering entrance tests, SSC JE, RRB JE, GATE, or other technical recruitment exams, these notes provide an excellent revision resource. Real-world engineering examples and step-by-step explanations help learners understand how force systems and equilibrium principles are applied in civil, mechanical, electrical, and production engineering.
Study Engineering Mechanics Section 3 to improve your analytical abilities, master static force analysis, and confidently solve numerical and objective questions that frequently appear in academic and competitive examinations.
1. 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
Correct Answer: A. same
2. The loss of kinetic energy during inelastic impact is given by(where m1 = Mass of the first body,m2 = Mass of the second body, and u1 and u2 = Velocities of the first and second bodies respectively.)
A. \( \frac{m_1m_2}{2(m_1+m_2)}(u_1-u_2)^2 \)
B. \( \frac{2(m_1+m_2)}{m_1m_2}(u_1-u_2)^2 \)
C. \( \frac{m_1m_2}{2(m_1+m_2)}(u_1^2-u_2^2) \)
D. \( \frac{2(m_1+m_2)}{m_1m_2}(u_1^2-u_2^2) \)
Correct Answer: Option A
3. The centre of gravity of a hemisphere lies at a distance of 3r / 8 from its base measured along the vertical radius.
A. Correct
B. Incorrect
Correct Answer: A. Correct
4.
The above figure shows the three coplanar forces P, Q and R acting at a point O. If these forces are in equilibrium, then
A. \( \frac{P}{\sin\beta}=\frac{Q}{\sin\alpha}=\frac{R}{\sin\gamma} \)
B. \( \frac{P}{\sin\alpha}=\frac{Q}{\sin\beta}=\frac{R}{\sin\gamma} \)
C. \( \frac{P}{\sin\gamma}=\frac{Q}{\sin\alpha}=\frac{R}{\sin\beta} \)
D. \( \frac{P}{\sin\alpha}=\frac{Q}{\sin\gamma}=\frac{R}{\sin\beta} \)
Correct Answer: Option B
5. 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. \( \frac{db^3}{12} \)
B. \( \frac{bd^3}{12} \)
C. \( \frac{db^3}{36} \)
D. \( \frac{bd^3}{36} \)
Correct Answer: Option A
6. The polygon law of forces states that if a number of forces, acting simultaneously on a particle, be represented in magnitude and direction by the sides a polygon taken in order, then their resultant is represented in magnitude and direction by the closing side of the polygon, taken in opposite direction.
A. Correct
B. Incorrect
Correct Answer: A. Correct
7. A smooth cylinder lying on a __________ is in neutral equilibrium.
A. curved surface
B. convex surface
C. horizontal surface
Correct Answer: C. horizontal surface
8. 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. \( \omega\sqrt{y^2-r^2} \)
B. \( \omega\sqrt{r^2-y^2} \)
C. \( \omega^2\sqrt{y^2-r^2} \)
D. \( \omega^2\sqrt{r^2-y^2} \)
Correct Answer: Option B
9. 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.
Correct Answer: D. the algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point.
10. 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 the coefficient of friction.
A. increase
B. decrease
C. not be affected
Correct Answer: A. increase
11. 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 δ = Deflection of the spring.)
A. \(2\pi\sqrt{\frac{g}{\delta}}\)
B. \(\frac{1}{2\pi}\sqrt{\frac{g}{\delta}}\)
C. \(2\pi\sqrt{\frac{\delta}{g}}\)
D. \(\frac{1}{2\pi}\sqrt{\frac{\delta}{g}}\)
Correct Answer: Option B
12. The angle of inclination with the vertical is __________ if the cyclist is running at a faster speed than that when he is running at a slower speed.
A. more
B. less
Correct Answer: A. more
13. The range of projectile(R) on an upward inclined plane is
A. \( \frac{g\cos^2\beta}{2u^2\sin(\alpha+\beta)\cos\alpha} \)
B. \( \frac{2u^2\sin(\alpha+\beta)\cos\alpha}{g\cos^2\beta} \)
C. \( \frac{g\cos^2\beta}{2u^2\sin(\alpha-\beta)\cos\alpha} \)
D. \( \frac{2u^2\sin(\alpha-\beta)\cos\alpha}{g\cos^2\beta} \)
Correct Answer: Option D
14. The center 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
Correct Answer: C. h/4
15. In actual machines, mechanical advantage is __________ velocity ratio.
A. equal to
B. less than
C. greater than
Correct Answer: B. less than
16. The radius of gyration is the distance where the whole mass (or area) of a body is assumed to be concentrated.
A. Correct
B. Incorrect
Correct Answer: A. Correct
17. If three coplanar forces acting on a point are in equilibrium, then each force is proportional to the sine, of the angle between the other two.
A. Correct
B. Incorrect
Correct Answer: A. Correct
18. A rubber ball is dropped from a height of 2 m. If there is no loss of velocity after rebounding, the ball will rise to a height of
A. 1m
B. 2m
C. 3m
D. 4m
Correct Answer: B. 2m
19. In the shown figure, the tension (T) in the string will be
A. \( \frac{m_1m_2g}{m_1+m_2} \)
B. \( \frac{2m_1m_2g}{m_1+m_2} \)
C. \( \frac{m_1+m_2}{m_1m_2g} \)
D. \( \frac{m_1+m_2}{m_1m_2g} \)
Correct Answer: Option B
20. When the spring of a watch is wound, it will possess
A. strain energy
B. kinetic energy
C. heat energy
D. electrical energy
Correct Answer: A. strain energy
21. In a framed structure, as shown in the below figure, the force in the member CD is tensile in nature.
A. Agree
B. Disagree
Correct Answer: A. Agree
22. An irregular body may have more than one centre of gravity.
A. Yes
B. No
Correct Answer: B. No
23. The rate of doing work is known as
A. potential energy
B. kinetic energy
C. power
D. none of these
Correct Answer: C. power
24. In a wormed geared pulley block, if the number of teeth on the worm wheel is doubled, then its velocity ratio is also doubled.
A. True
B. False
Correct Answer: A. True
25. Moment of inertia of a circular section about its diameter (d) is
A. πd3/16
B. πd3/32
C. πd4/32
D. πd4/64
Correct Answer: D. πd4/64
26. The centre of oscillation and centre of suspension for a compound pendulum are interchangeable.
A. True
B. False
Correct Answer: A. True
27. In a screw jack, the effort required to lower the load is __________ the effort required to raise the same load.
A. less than
B. equal to
C. more than
Correct Answer: A. less than
28. The unit of work in S.I. units is
A. Newton
B. Erg
C. kg-m
D. Joule
Correct Answer: D. Joule
29. 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
Correct Answer: D. all of the above
30. The maximum height of a projectile on a horizontal plane is
A. \( \frac{u^2\sin^2\alpha}{2g} \)
B. \( \frac{u^2\cos^2\alpha}{2g} \)
C. \( \frac{u^2\sin^2\alpha}{g} \)
D. \( \frac{u^2\cos^2\alpha}{g} \)
Correct Answer: Option A
31. The acceleration of a particle moving with simple harmonic motion is __________ at the mean position.
A. zero
B. minimum
C. maximum
Correct Answer: A. zero
32. The velocity of a particle moving with simple harmonic motion is __________ at the mean position.
A. zero
B. minimum
C. maximum
Correct Answer: C. maximum
33. A framed structure is imperfect, if the number of members are __________ (2j - 3).
A. equal to
B. less than
C. greater than
D. either (b) or (c)
Correct Answer: D. either (b) or (c)
34. The linear acceleration (a) of a body rotating along a circular path of radius (r) with an angular acceleration of α rad / s2, is
A. a = α/ r
B. a = α.r
C. a = r / α
D. none of these
Correct Answer: B. a = α.r
35. The total energy possessed by a system of moving bodies
A. is constant at every instant
B. varies from point to point
C. is maximum in the start and minimum at the end
D. is minimum in the start and maximum at the end
Correct Answer: A. is constant at every instant
36. The moment of inertia of a solid cylinder of mass m, radius r and length l about the longitudinal axis or polar axis is
A. mr2/2
B. mr2/4
C. mr2/6
D. mr2/8
Correct Answer: A. mr2/2
37. In a screw jack, the effort required to lift the load is given by(where W = Load lifted, α = Helix angle, and φ = Angle of friction.)
A. P = W tan (α - φ)
B. P = W tan (α + φ)
C. P = W tan (φ - α)
D. P = W cos (α + φ)
Correct Answer: B. P = W tan (α + φ)
38. The terms 'leverage' and 'mechanical advantage' Of a compound lever have got the same meaning.
A. Correct
B. Incorrect
Correct Answer: A. Correct
39. A couple produces
A. translatory motion
B. rotational motion
C. combined translatory and rotational motion
D. none of the above
Correct Answer: B. rotational motion
40. Energy may be defined as the capacity of doing work.
A. Correct
B. Incorrect
Correct Answer: A. Correct
41. For a self-locking machine, the efficiency must be
A. equal to 50%
B. less than 50%
C. greater than 50%
D. 100%
Correct Answer: B. less than 50%
42. 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
Correct Answer: B. Q = R
43. One joule is equal to
A. 0.1 N-m
B. 1 N-m
C. 10 N-m
D. 100 N-m
Correct Answer: B. 1 N-m
44. Whenever a force acts on a body and the body undergoes a displacement, then
A. work is said to be done
B. power is being transmitted
C. body has a kinetic energy of translation
D. none of these
Correct Answer: A. work is said to be done
45. When a particle moves along a straight path, there will be centripetal acceleration as well as tangential acceleration.
A. Correct
B. Incorrect
Correct Answer: B. Incorrect
46. 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
Correct Answer: C. +9.8 m/s2
47. A framed structure, as shown in the below figure, is a
A. perfect frame
B. deficient frame
C. redundant frame
D. none of the above
Correct Answer: A. perfect frame
48. The rate of change of displacement of a body is called
A. velocity
B. acceleration
C. momentum
D. none of these
Correct Answer: A. velocity
49. The efficiency of a screw jack is maximum, when(where α = Helix angle, and φ = Angle of friction.)
A. α = 45° + φ/2
B. α = 45° - φ/2
C. α = 90° + φ
D. α = 90° - φ
Correct Answer: B. α = 45° - φ/2
50. The periodic time (T) is given by(where ω = Angular velocity of particle in rad / s.)
A. ω/2π
B. 2π/ω
C. 2π x ω
D. π/ω
Correct Answer: B. 2π/ω
