SOLUTION OF PRESEMESTER EXAMINATION: ENGINEERING MECHANICS SOLUTION OF PRESEMESTER EXAMINATION: ENGINEERING MECHANICS©subhankar_karmakar

GROUP-A Q.1 Answer the following questions as per the instructions 2x20=20 Choose the correct answer of the following questions: (i) A truss hinged at one end, supported on rollers at the other, is subjected to horizontals load only. Its reaction at the hinged end will be (a) Horizontal;                   (b) Vertical (c) Both horizontal & vertical (d) None of the above. Ans: (c) both horizontal & vertical (ii) The moment of inertia of a circular section of diameter D about its centroidal axis is given by the expression (a) π(D)4/16           (b) π(D)4/32 (c) π(D)4/64           (d) π(D)4/4 Ans: (c) π(D)4/64 Fill in the blanks in the following questions: (iii)The distance of the centroid of an equilateral triangle with each side(a) is …………. from any of the three sides. Ans a /(2√3) (iv)Poisson’s ratio is defined as the ratio between ……. and ………… . Ans: Lateral Strain, Longitudinal Strain (v)If two forces of equal magnitudes P having an angle 2Ө between them, then their resultant force will be equal to ________ . Ans: 2P CosӨ Choose the correct word/s. (vi) Two equal and opposite force acting at different points of a rigid body is termed as (Bending Moment/ Torque/ Couple). Ans: Couple

Choose correct answer for the following parts: (vii) Statement 1: In stress strain graph of a ductile material, yield point starts at the end of the elastic limit. Statement 2: At yielding point, the deformation becomes plastic by nature. (a) Statement 1 is true, Statement 2 is true. (b) Statement 1 is true, Statement 2 is true and they are unrelated with each other (c) Statement 1 is true, statement 2 is false. (d) Statement 1 is false, Statement 2 is false. Ans: (a) Statement 1 is true, Statement 2 is true. (viii) Statement 1: It is easier to pull a body on a rough surface than to push the body on the same surface. Statement 2: Frictional force always depends upon the magnitude of the normal force. (a) Statement 1 is true, Statement 2 is true. (b) Statement 1 is true, Statement 2 is true and they are unrelated (c) Statement 1 is true, statement 2 is false. (d) Statement 1 is false, Statement 2 is false. Ans: (a) Statement 1 is true, Statement 2 is true. (ix) In a cantilever bending moment is maximum at (a) free end            (b) fixed end (c) at the mid span (d) none of these Ans: (b) fixed end (x) The relationship between linear velocity and angular velocity of a cycle (a) exists under all conditions (b) does not exist under all conditions (c) exists only when it moves on horizontal plane. (d) none of these Ans: (a) exists under all conditions

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SOLUTION OF PRESEMESTER EXAMINATION: ENGINEERING MECHANICS PART-II ©subhankar_karmakar

MULTIPLE CHOICE QUESTIONS: ENGINEERING MECHANICS

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ENGINEERING MECHANICS & STRENGTH OF MATERIALS – MCQ THINKING GUIDE

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🧠 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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