INTELLIGENT OBJECTIVE QUESTIONS IN MECHANICS

1) A cantilever beam of square cross-section (100 mm X 100 mm) and length 2 m carries a concentrated load of 5 kN at its free end. What is the maximum normal bending stress at its mid-length cross-section?

(a) 10 N/mm²
(b) 20 N/mm²
(c) 30 N/mm²
(d) 40 N/mm²

2) A hollow shaft of outside diameter 40 mm and inside diameter 20 mm is to replaced by a solid shaft of 30 mm diameter. If the maximum shear stresses induced in the two shafts are to be equal, what is the ratio of the maximum resistible torque in the hollow to that of solid shaft?

(a) 10/9
(b) 20/9
(c) 30/9
(d) 40/9

(3) A cannonball is fired from a tower 80 m above the ground with a horizontal velocity of 100 m/s. Determine the horizontal distance at which the ball will hit the ground. (take g=10 m/s²)

(a) 400 m,
(b) 280 m,
(c) 200 m,
(d) 100 m.

(4) Water drops from a tap at the rate of four droplets per second. Determine the vertical separation between two consecutive drops after the lower drop attained a velocity of 4 m/s. Take g=10 m/s².

(a) 0.49 m
(b) 0.31 m
(c) 0.50 m
(d) 0.30 m

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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