QUESTIONS BANK 5 : FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

 

QUESTIONS BANK 4 : FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

QUESTIONS BANK 3 : FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

 

QUESTIONS BANK 2: FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

1)      Explain the principle of Super-position.

Ans: The principle of superposition states that “The effect of a force on a body does not change and remains same if we add or subtract any system which is in equilibrium.”

In the fig 4 a, a force P is applied at point A in a beam, where as in the fig 4 b, force P is applied at point A and a force system in equilibrium which is added at point B. Principle of super position says that both will produce the same effect.

2)      What is “Force-Couple system?”

Ans: When a force is required to transfer from a point A to point B, we can transfer the force directly without changing its magnitude and direction but along with the moment of force about point B.

As a result of parallel transfer a system is obtained which is always a combination of a force and a moment or couple. This system consists of a force and a couple at a point is known as Force-Couple system.

      In fig 5 a, a force P acts on a bar at point A, now at point B we introduce a system of forces  in equilibrium (fig 5 b), hence according to principle of superposition there is no change in effect of the original system. Now we can reduce the downward force P at point A and upward force P at point B as a couple of magnitude Pxd at point B (fig 5 c).

3) What do you understand by Equivalent force systems?

Ans: Two different force systems will be equivalent if they can be reduced to the same force-couple system at a given point. So, we can say that two force systems acting on the same rigid body will be equivalent if the sums of forces or resultant and sums of the moments about a point are equal.

4)      What is orthogonal or perpendicular resolution of a force?

Ans: The resolution of a force into two components which are mutually perpendicular to each other along X-axis and Y-axis is called orthogonal resolution of a force.

If a force F acts on an object at an angle θ with the positive X-axis, then its component along X-axis is F_x = Fcosθ, and that along Y-axis is F_y = Fsinθ

5) What is oblique or non-perpendicular resolution of a force?

Ans: When a force is required to be resolved in to two directions which are not perpendiculars to each other the resolution is called oblique or Non-perpendicular resolution of a force.

   
       F_OA = (P sin β)/ sin (α +β)

 F_OB = (P sin α)/ sin (α +β)

QUESTION BANK 1: FORCE AND FORCE SYSTEM

(I am going to publish a question bank for EME-102/EME-202 of 1st yr. MTU; Greater Noida. Some pages from the book .......Subhankar Karmakar)

QUESTION BANK: ENGINEERING MECHANICS

by Er. Subhankar Karmakar

Unit: 1 (Force System)

VERY SHORT QUESTIONS (2 marks):

1)      What is force and force system?

Ans: A force is a physical quantity having magnitude as well as direction. Therefore, it is a   vector quantity. It is defined as an "external agency" which produces or tends to produce or destroys or tends to destroy the motion when applied on a body.

Its unit is Newton (N) in S.I. systems and dyne in C.G.S. system.

When two or more forces act on a body or particle, it is called force system. Therefore, a force system is a collection of two or more forces.

2)      What is static equilibrium? What are the different types of static equilibrium?

Ans: A body is said to be in static equilibrium when there is no change in position as well as no rotation exist on the body. So to be in equilibrium process, there must not be any kind of motions ie there must not be any kind of translational motion as well as rotational motion.

We also know that to have a linear translational motion we need a net force acting on the object towards the direction of motion, again to induce an any kind of rotational motion, a net moment must exists acting on the body. Further it can be said that any kind of complex motion can be resolved into a translational motion coupled with a rotating motion.

“Therefore a body subjected to a force system would be at rest if and only if the net force as well as the net moment on the body is zero.”

There are three types of Static Equilibrium

1.      Stable Equilibrium

2.      Unstable Equilibrium

3.      Neutral Equilibrium

3)      What are the characteristics of a force?

Ans: A force has four (4) basic characteristics.

·         Magnitude: It is the value of the force. It is represented by the length of the arrow that we use to represent a force.

·         Direction: A force always acts along a line, which is called as the “line of action”. The arrow head we used to represent a force is the direction of that force.

·         Nature or Sense: The arrow head also represent the nature of a force. A force may be a pull or a push. If a force acts towards a particle it will be a push and if the force acts away from a point it is pull.

·         Point of Application: It is the original location of a point on a body where the force is acting. 

4)      What are the effects of a force acting on a body?

Whenever a force acts on a body or particle, it may produce some external as well as internal effects or changes.

·         A force may change the state or position of a body by inducing motion of the body. (External effect)

·         A force may change the size or shape of an object when applied on it. It may deform the body thus inducing internal effects on the body.

·         A force may induce rotational motion into a body when applied at a point other than its center of gravity.

·         A force can make a moving body into an equilibrium state at rest.

5)      What is composition and resolution of forces?

Ans: Composition of forces: Composition or compounding is the procedure to find out single resultant force of a force system

Resolution of forces: Resolution is the procedure of splitting up a single force into number of components without changing the effect of the same.

6)      What is Resultant and Equilibrant?

Ans: Resultant: The resultant of a force system is the Force which produces same effect as the combined forces of the force system would do. So if we replace all components of the force by the resultant force, then there will be no change in effect.

The Resultant of a force system is a vector addition of all the components of the force system. The magnitude as well as direction of a resultant can be measured through analytical method.

Equilibrant: Any concurrent set of forces, not in equilibrium, can be put into a state of equilibrium by a single force. This force is called the Equilibrant. It is equal in magnitude, opposite in sense and co-linear with the resultant. When this force is added to the force system, the sum of all of the forces is equal to zero.

7)      Explain the principle of Transmissibility?

Ans: The principle of transmissibility states “the point of application of a force can be transmitted anywhere along the line of action, but within the body.”

The fig 3 a shows a force F acting at a point of application A and fig 3 b, the same force F acts along the same line of action but at a different point of action at B and both are equivalent to each other.

NEW SYLLABUS FOR ENGINEERING MECHANICS: FIRST YEAR OF MTU FOR 2012-13

ENGINEERING MECHANICS

L T P

3 1 2

UNIT I

Two Dimensional Concurrent Force Systems: Basic concepts, Units, Force systems, Laws of motion, Moment and Couple, Vectors - Vector representation of forces and moments - Vector operations. Principle of Transmissibility of forces, Resultant of a force system, Equilibrium and Equations of equilibrium, Equilibrium conditions, Free body diagrams, Determination of reaction, Resultant of two dimensional concurrent forces, Applications of concurrent forces.                                                                     8

UNIT II
Two Dimensional Non-Concurrent Force Systems: Basic Concept, Varignon’s theorem, Transfer of a Force to Parallel Position, Distributed force system, Types of Supports and their Reactions, Converting force into couple and vise versa.                                                                                                                   3
Friction: Introduction, Laws of Coulomb Friction, Equilibrium of bodies involving dry-friction, Belt friction, Ladder Friction, Screw jack                                                                                                         3
Structure: Plane truss, Perfect and Imperfect Truss, Assumption in the Truss Analysis, Analysis of Perfect Plane Trusses by the Method of Joints, Method of Section.                                                           4


UNIT III
Centroid and Moment of Inertia: Centroid of plane, curve, area, volume and composite bodies,
Moment of inertia of plane area, Parallel Axes Theorem, Perpendicular axes theorems, Mass Moment of Inertia of Circular Ring, Disc, Cylinder, Sphere and Cone about their, Axis of Symmetry. Pappus-theorems, Polar moment of inertia.                                                                                                               8

UNIT IV
Kinematics of Rigid Body: Introduction, Plane Rectilinear Motion of Rigid Body, Plane Curvilinear Motion of Rigid Body, Velocity and Acceleration under Translation and Rotational Motion, Relative Velocity. 8


UNIT (V)
Kinetics of Rigid Body: Introduction, Force, Mass and Acceleration, Work and Energy, Impulse and Momentum, D’Alembert’s Principles and Dynamic Equilibrium, Friction in moving bodies.              8

Text books:
1. Engineering Mechanics Statics , J.L Meriam , Wiley
2. Engineering Mechanics Dynamics , J.L Meriam , Wiley
3. Engineering Mechanics – Statics & Dynamics by A Nelson, McGraw Hill
4. Engineering Mechanics : Statics and Dynamics, R. C. Hibbler
5. Mechanics of Solids by Abdul Mubeen, Pearson Education Asia.
6. Mechanics of Materials by E.P.Popov, Prentice Hall of India Private Limited.



ENGINEERING MECHANICS- LAB

(Any 10 experiments of the following or such experiments suitably designed)

1. Polygon law of Co-planer forces (concurrent)
2. Bell crank lever -Jib crane
3. Support reaction for beam
4. Collision of elastic bodies(Law of conservation of momentum
5. Moment of inertia of fly wheel.
6. Screw fiction by using screw jack
7. To study the slider-crank mechanism etc. of 2-stroke & 4-stroke I.C. Engine models.
8. Friction experiment(s) on inclined plane and/or on screw-jack.
9. Simple & compound gear-train experiment.
10. Worm & worm-wheel experiment for load lifting.
11. Belt-Pulley experiment. .
12. Experiment on Trusses.
13. Statics experiment on equilibrium
14. Dynamics experiment on momentum conservation
15. Dynamics experiment on collision for determining coefficient of restitution.
16. Simple/compound pendulum

MULTIPLE CHOICE QUESTIONS: ENGINEERING MECHANICS

  Edunes Online Education

ENGINEERING MECHANICS & STRENGTH OF MATERIALS – MCQ THINKING GUIDE

Edunes Online Education

🧠 Strategy: First understand the physical principle → Then eliminate wrong options → Then confirm formula.

Q1) In a simply supported beam of length L, a UDL of w kN/m acts on the entire span. The maximum bending moment will be:

a) wL²/8
b) wL³/8
c) wL²/4
d) wL³/4

UDL over full span → Maximum BM at mid-span. Standard formula:

✅ (a) wL² / 8

🧠 Simply supported + UDL → “L² over 8”

Q2) If two forces are acting on a particle and the particle is in stable equilibrium, then the forces are:

a) Equal to each other
b) Equal but opposite in direction
c) Unequal but same direction
d) None of the above

For equilibrium under two forces: Equal magnitude + Opposite direction + Same line of action.

✅ (b) Equal but opposite in direction

🧠 Only two forces? → They must cancel perfectly.

Q3) The example of statically indeterminate structures are:

a) Continuous beam
b) Cantilever beam
c) Over-hanging beam
d) Both cantilever and fixed beam

Indeterminate → More unknown reactions than equilibrium equations. Continuous beam has extra supports.

✅ (a) Continuous beam

🧠 Extra supports = Extra unknowns = Indeterminate

Q4) A redundant truss satisfies:

a) m = 2j − 3
b) m < 2j + 3
c) m > 2j − 3
d) m > 2j + 3

Perfect truss: m = 2j − 3 More members → Redundant

✅ (c) m > 2j − 3

🧠 “More members than needed” = Redundant

Q5) Property of a material to withstand sudden shock is:

a) Hardness
b) Ductility
c) Toughness
d) Elasticity

Shock → Energy absorption → Toughness.

✅ (c) Toughness

🧠 Impact resistance = Toughness

Q6) Stress generated by a dynamic loading is approximately ____ times the stress developed by gradually applying the same load.

Suddenly applied load causes double stress.

✅ 2 times

🧠 Sudden load → Double stress

Q7) The ratio between volumetric stress and volumetric strain is:

a) Young's modulus
b) Modulus of elasticity
c) Rigidity modulus
d) Bulk modulus

Volume change relation → Bulk modulus.

✅ (d) Bulk modulus

🧠 Volume → Bulk modulus

Q8) In a cantilever beam, maximum bending moment is induced at:

a) Free end
b) Fixed end
c) Mid span
d) None of the above

Cantilever fixed at one end → Maximum BM at fixed support.

✅ (b) At the fixed end

🧠 Cantilever cries at fixed end.

Q9) Forces which meet at a point are called:

a) Collinear forces
b) Concurrent forces
c) Coplanar forces
d) Parallel forces

Concurrent → Intersect at one point.

✅ (b) Concurrent forces

🧠 Meet at one point → Concurrent

Q10) The coefficient of friction depends upon:

a) Nature of the surface
b) Shape of the surface
c) Area of contact
d) Weight of body

Independent of area & weight. Depends on surface nature.

✅ (a) Nature of the surface

🧠 Roughness matters. Area doesn’t.

Q11) Variation of shear force due to triangular load on simply supported beam is:

a) Uniform
b) Linear
c) Parabolic
d) Cubic

Load is linear → Shear is integral → Parabolic.

✅ (c) Parabolic

🧠 Load linear → Shear parabolic → BM cubic

Q12) A body is on the point of sliding down a 30° inclined plane. Coefficient of friction is:

a) \( (\frac{1}{3})^{\frac{1}{2}} \)
b) √3
c) 1
d) 0

At limiting equilibrium: μ = tanθ
μ = tan30° = 1/√3

✅ (a) \( (\frac{1}{3})^{\frac{1}{2}} \)

🧠 On verge of sliding → μ = tanθ

FINAL NEURAL COMPRESSION TABLE

Concept	Quick Memory Code
UDL BM	wL²/8
Sudden Load	2 × Stress
Perfect Truss	m = 2j − 3
Friction Limit	μ = tanθ

🧠 When formula connects with physical meaning, MCQs become recognition — not rote memory.

ENGINEERING MECHANICS & SOM – MCQ PRACTICE SET 2

🧠 Think Like an Engineer: Every MCQ is testing one core law: Equilibrium • Compatibility • Constitutive relation • Load–Shear–Moment relation

Q1) For a simply supported beam with a central point load W, the maximum bending moment is:

a) WL/2
b) WL/4
c) WL/8
d) WL²/8

Central point load → Maximum BM at mid-span. Standard formula:

✅ (b) WL / 4

🧠 Point load center → “L over 4”

Q2) A body is said to be in equilibrium when:

a) Only ∑F = 0
b) Only ∑M = 0
c) ∑F = 0 and ∑M = 0
d) Acceleration is constant

Static equilibrium requires:

1. Sum of forces = 0
2. Sum of moments = 0

✅ (c) ∑F = 0 and ∑M = 0

🧠 No translation + No rotation = Equilibrium

Q3) A cantilever beam carrying a point load at free end has maximum shear force at:

a) Free end
b) Fixed end
c) Mid span
d) Zero everywhere

Shear force is maximum at fixed support.

✅ (b) Fixed end

🧠 Cantilever suffers at the fixed end.

Q4) For a perfect frame (plane truss), the relation between members (m) and joints (j) is:

a) m = 2j + 3
b) m = 2j − 3
c) m = j − 3
d) m = 3j − 2

Condition of perfect truss:

✅ (b) m = 2j − 3

🧠 Perfect truss = 2j minus 3

Q5) The ratio of lateral strain to longitudinal strain is called:

a) Young’s modulus
b) Bulk modulus
c) Poisson’s ratio
d) Rigidity modulus

Lateral contraction / Axial extension

✅ (c) Poisson’s ratio

🧠 Stretch long → Shrink sideways → Poisson

Q6) The bending moment at the free end of a cantilever beam is:

a) Maximum
b) Minimum
c) Zero
d) Infinite

Free end cannot resist moment.

✅ (c) Zero

🧠 Free end = Free from moment.

Q7) If load intensity is constant, the shear force diagram will be:

a) Linear
b) Parabolic
c) Cubic
d) Constant

UDL is constant → Shear force varies linearly.

✅ (a) Linear

🧠 Load constant → Shear straight line

Q8) The strain energy stored in a body depends upon:
a) Load only
b) Stress only
c) Stress and strain
d) Volume only

Strain energy = (1/2) × stress × strain × volume

✅ (c) Stress and strain

🧠 Energy lives where stress meets strain.

Q9) The angle of friction is defined as:

a) Angle between normal reaction and resultant reaction
b) Angle between weight and plane
c) Angle between friction and plane
d) Angle of slope

Angle between resultant reaction and normal reaction.

✅ (a)

🧠 Resultant reaction tilts by angle of friction.

Q10) A beam subjected to pure bending experiences:

a) Shear stress only
b) Normal stress only
c) Both shear and normal stress
d) No stress

Pure bending → No shear force → Only bending stress.

✅ (b) Normal stress only

🧠 Pure bending → Pure normal stress.

Q11) The modulus of rigidity relates:

a) Normal stress & longitudinal strain
b) Shear stress & shear strain
c) Volumetric stress & volumetric strain
d) Bending stress & curvature

Rigidity modulus (G) → Shear relationship.

✅ (b) Shear stress & shear strain

🧠 Rigidity = Resistance to shear.

Q12) A simply supported beam with no external load will have:

a) Zero shear and zero bending moment
b) Maximum shear
c) Maximum bending moment
d) Uniform moment

No load → No reactions → No internal forces.

✅ (a) Zero shear and zero bending moment

🧠 No load → No stress → Peaceful beam.

FINAL PATTERN MAP

Topic	Core Trigger
Simply Supported (Point Load)	WL/4
Perfect Truss	m = 2j − 3
Friction Limit	μ = tanθ
Pure Bending	No shear stress

🧠 When you see the question, ask: “Which law is hiding here?” That is how toppers think.

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