MECHANICS OF MATERIALS

MCQ question all unit

1. Stress is defined as:
A. Load × Area
B. Load / Volume
C. Load / Area
D. Area / Load
✅ Correct Answer: C. Load / Area

2. The SI unit of stress is:

A. N
B. N/m
C. N/m²
D. N·m
✅ Correct Answer: C. N/m² (also called Pascal)

3. Strain is:
A. Force per unit area
B. Deformation per unit length
C. Load × Area
D. Change in stress
✅ Correct Answer: B. Deformation per unit length

4. The ratio of lateral strain to longitudinal strain is called:

A. Young’s modulus
B. Bulk modulus
C. Poisson’s ratio
D. Shear modulus
✅ Correct Answer: C. Poisson’s ratio

5. Hooke’s Law is valid:

A. Only for liquids
B. After yield point
C. Within elastic limit
D. For all materials
✅ Correct Answer: C. Within elastic limit

6. The Young’s modulus is defined as the ratio of:

A. Shear stress to shear strain
B. Lateral strain to axial strain
C. Tensile stress to tensile strain
D. Stress to bulk strain
✅ Correct Answer: C. Tensile stress to tensile strain
7. A bar of cross-sectional area A and length L is subjected to axial tensile force P. The
elongation ΔL is given by:
A. P⋅LA⋅E\frac{P \cdot L}{A \cdot E}A⋅EP⋅L
B. A⋅LP⋅E\frac{A \cdot L}{P \cdot E}P⋅EA⋅L
C. PA⋅L\frac{P}{A \cdot L}A⋅LP
D. PE\frac{P}{E}EP
✅ Correct Answer: A. P⋅LA⋅E\frac{P \cdot L}{A \cdot E}A⋅EP⋅L

8. The unit of Young’s modulus is:

A. N
B. N/m
C. N/m²
D. Dimensionless
✅ Correct Answer: C. N/m²
1. What is stress?
A. The ratio of force to volume
B. The internal resistance offered by a body to deformation
C. The deformation produced in a body
D. The force applied on a body
✅ Correct Answer: B. The internal resistance offered by a body to deformation

2. Which of the following best defines strain?

A. Load per unit area
B. Change in length per unit original length
C. Energy per unit volume
D. Change in area per unit force
✅ Correct Answer: B. Change in length per unit original length

3. The formula for normal stress (σ) is:

A. σ=FV\sigma = \frac{F}{V}σ=VF
B. σ=FA\sigma = \frac{F}{A}σ=AF
C. σ=F×AL\sigma = \frac{F \times A}{L}σ=LF×A
D. σ=LF\sigma = \frac{L}{F}σ=FL
✅ Correct Answer: B. σ=FA\sigma = \frac{F}{A}σ=AF

4. What is the unit of strain?

A. N/m²
B. m
C. Dimensionless
D. N
✅ Correct Answer: C. Dimensionless

5. Hooke's Law states that:

A. Stress is inversely proportional to strain
B. Stress is directly proportional to strain within the elastic limit
C. Strain is constant for all materials
D. Stress is independent of strain
✅ Correct Answer: B. Stress is directly proportional to strain within the elastic limit

6. Which of the following is a type of stress?

A. Plastic stress
B. Tensile stress
C. Viscous stress
D. Optical stress
✅ Correct Answer: B. Tensile stress

7. The region in the stress-strain curve where Hooke’s law is valid is called the:
A. Plastic region
B. Yield region
C. Elastic region
D. Fracture point
✅ Correct Answer: C. Elastic region

8. When a material returns to its original shape after the removal of load, the behavior is
called:
A. Plastic
B. Brittle
C. Elastic
D. Rigid
✅ Correct Answer: C. Elastic
1. A simply supported beam has:
A. Fixed support at both ends
B. Roller support at one end and hinge support at the other
C. Free support at both ends
D. Fixed and roller support
✅ Correct Answer: B. Roller support at one end and hinge support at the other

2. A cantilever beam is fixed at:

A. One end only
B. Both ends
C. Middle point
D. All supports
✅ Correct Answer: A. One end only

3. A beam supported at both ends and loaded at the center is known as:
A. Cantilever beam
B. Simply supported beam
C. Overhanging beam
D. Fixed beam
✅ Correct Answer: B. Simply supported beam
4. A beam extending beyond its support on one or both sides is called:
A. Cantilever beam
B. Overhanging beam
C. Continuous beam
D. Fixed beam
✅ Correct Answer: B. Overhanging beam

5. A continuous beam is one that:

A. Is simply supported on two supports
B. Has more than two supports
C. Is fixed at one end
D. Is loaded with point loads only
✅ Correct Answer: B. Has more than two supports

6. The load acting per unit length of a beam is called:

A. Point load
B. Uniformly distributed load (UDL)
C. Moment
D. Concentrated load
✅ Correct Answer: B. Uniformly distributed load (UDL)

7. A point load is:

A. Load distributed uniformly
B. Load acting over a length
C. Load acting at a specific point
D. Load with varying intensity
✅ Correct Answer: C. Load acting at a specific point

8. A uniformly varying load (UVL) is:

A. Load constant throughout
B. Load acting at a single point
C. Load that changes linearly over length
D. Load that acts in opposite directions
✅ Correct Answer: C. Load that changes linearly over length
1. Shear force at a section of a beam is defined as:
A. Sum of all moments to the left of the section
B. Algebraic sum of vertical forces to one side of the section
C. Rate of change of slope
D. Total force acting on the beam
✅ Correct Answer: B. Algebraic sum of vertical forces to one side of the section

2. Bending moment at a section is:

A. Sum of vertical forces
B. Product of axial force and area
C. Algebraic sum of moments about that section
D. Shear force per unit area
✅ Correct Answer: C. Algebraic sum of moments about that section

3. At the free end of a cantilever beam, the shear force is:

A. Zero
B. Maximum
C. Minimum
D. Infinite
✅ Correct Answer: A. Zero

4. The bending moment is maximum where:

A. Shear force is zero
B. Shear force is maximum
C. Slope is zero
D. Deflection is maximum
✅ Correct Answer: A. Shear force is zero

5. For a simply supported beam with a central point load, the maximum bending moment
occurs at:
A. Supports
B. Quarter span
C. Midspan
D. Just beside the supports
✅ Correct Answer: C. Midspan

6. In a simply supported beam with UDL (uniformly distributed load), the shear force
diagram is:
A. Constant
B. Parabolic
C. Triangular
D. Linear
✅ Correct Answer: D. Linear

7. The unit of bending moment is:

A. N
B. N/m
C. N·m
D. N/m²
✅ Correct Answer: C. N·m

8. In a cantilever beam with a point load at the free end, the maximum bending moment
occurs at:
A. The free end
B. The point of application of load
C. At the fixed end
D. At mid-span
✅ Correct Answer: C. At the fixed end
1. The centroid of a plane figure is the point where:
A. All forces act
B. The moment of inertia is maximum
C. The area is zero
D. The whole area of the figure is assumed to be concentrated
✅ Correct Answer: D. The whole area of the figure is assumed to be concentrated

2. The centroid of a uniform semicircular lamina lies at a distance of:

A. 4r3π\frac{4r}{3\pi}3π4r from the flat side
B. 3r4π\frac{3r}{4\pi}4π3r from the curved side
C. 2rπ\frac{2r}{\pi}π2r from the flat side
D. rrr from the center
✅ Correct Answer: A. 4r3π\frac{4r}{3\pi}3π4r from the flat side

3. The centroid of a triangle lies at the point of intersection of its:

A. Bisectors
B. Altitudes
C. Medians
D. Perpendicular bisectors
✅ Correct Answer: C. Medians

4. The coordinates of the centroid of a rectangle of base b and height h (with origin at the
bottom-left corner) are:
A. (0,0)(0, 0)(0,0)
B. (b,h)(b, h)(b,h)
C. (b2,h2)\left(\frac{b}{2}, \frac{h}{2}\right)(2b,2h)
D. (b3,h3)\left(\frac{b}{3}, \frac{h}{3}\right)(3b,3h)
✅ Correct Answer: C. (b2,h2)\left(\frac{b}{2}, \frac{h}{2}\right)(2b,2h)

5. The centroid of a symmetrical object lies:

A. On its base
B. At its maximum height
C. Along its axis of symmetry
D. Always on the x-axis
✅ Correct Answer: C. Along its axis of symmetry

6. The centroid of a circular lamina lies:

A. At the center of the circle
B. On the circumference
C. On the diameter
D. Outside the circle
✅ Correct Answer: A. At the center of the circle
7. For a composite shape, the centroid is found using:
A. Integration only
B. Geometric assumptions
C. Weighted average of individual centroids
D. By guessing location
✅ Correct Answer: C. Weighted average of individual centroids

8. The coordinates of the centroid (xˉ,yˉ)(x̄, ȳ)(xˉ,yˉ) of a composite area are calculated as:
A. ∑Ai∑xi+yi\frac{\sum A_i}{\sum x_i + y_i}∑xi+yi∑Ai
B. ∑(xi+yi)\sum (x_i + y_i)∑(xi+yi)
C. ∑(Aixi)∑Ai,∑(Aiyi)∑Ai\frac{\sum (A_i x_i)}{\sum A_i}, \frac{\sum (A_i y_i)}{\sum
A_i}∑Ai∑(Aixi),∑Ai∑(Aiyi)
D. A×xA \times xA×x, A×yA \times yA×y
✅ Correct Answer: C. ∑(Aixi)∑Ai,∑(Aiyi)∑Ai\frac{\sum (A_i x_i)}{\sum A_i}, \frac{\sum
(A_i y_i)}{\sum A_i}∑Ai∑(Aixi),∑Ai∑(Aiyi)
1. Moment of Inertia (MOI) of a plane area represents:
A. Resistance to axial force
B. Resistance to torsion
C. Resistance to bending
D. Center of gravity location
✅ Correct Answer: C. Resistance to bending

2. The unit of moment of inertia (area) in SI units is:

A. m
B. m²
C. m⁴
D. Nm
✅ Correct Answer: C. m⁴

3. Moment of inertia of a rectangle about its base (b × h) is:

A. bh22\frac{bh^2}{2}2bh2
B. bh33\frac{bh^3}{3}3bh3
C. b2h3\frac{b^2h}{3}3b2h
D. b3h3\frac{b^3h}{3}3b3h
✅ Correct Answer: B. bh33\frac{bh^3}{3}3bh3

4. Moment of inertia of a triangle about its base is:

A. bh33\frac{bh^3}{3}3bh3
B. bh22\frac{bh^2}{2}2bh2
C. bh312\frac{bh^3}{12}12bh3
D. bh336\frac{bh^3}{36}36bh3
✅ Correct Answer: D. bh336\frac{bh^3}{36}36bh3

5. The parallel axis theorem is used when:

A. Axis passes through the centroid
B. Axis is inclined to the centroidal axis
C. Axis is shifted parallel to the centroidal axis
D. Axis is perpendicular to the plane
✅ Correct Answer: C. Axis is shifted parallel to the centroidal axis

6. According to the parallel axis theorem:

A. I=Ic−Ad2I = I_c - Ad^2I=Ic−Ad2
B. I=Ic+AdI = I_c + AdI=Ic+Ad
C. I=Ic+Ad2I = I_c + Ad^2I=Ic+Ad2
D. I=Ic−AdI = I_c - AdI=Ic−Ad
✅ Correct Answer: C. I=Ic+Ad2I = I_c + Ad^2I=Ic+Ad2

7. For a circular section of radius rrr, the moment of inertia about its diameter is:
A. πr44\frac{\pi r^4}{4}4πr4
B. πr22\frac{\pi r^2}{2}2πr2
C. πr464\frac{\pi r^4}{64}64πr4
D. πr48\frac{\pi r^4}{8}8πr4
✅ Correct Answer: C. πr44\frac{\pi r^4}{4}4πr4 about center;
✅ Note: For diameter axis (x or y), it's C. πr44/4=πr464\frac{\pi r^4}{4}/4 = \frac{\pi
r^4}{64}4πr4/4=64πr4

8. The moment of inertia of a composite section is obtained by:

A. Adding areas of individual parts
B. Multiplying all individual moments
C. Summing individual moments using the parallel axis theorem
D. Dividing each part’s moment by area
✅ Correct Answer: C. Summing individual moments using the parallel axis theorem
1. The moment of inertia of a body depends on:
A. Mass only
B. Distribution of mass only
C. Axis of rotation only
D. Mass and distribution of mass about the axis
✅ Answer: D. Mass and distribution of mass about the axis

2. The SI unit of moment of inertia is:

A. kg·m/s²
B. kg·m²
C. N·m
D. m²/s
✅ Answer: B. kg·m²

3. Moment of inertia of a thin rod of mass MMM and length LLL about an axis through its center
and perpendicular to its length is:
A. 112ML2\frac{1}{12} ML^2121ML2
B. 13ML2\frac{1}{3} ML^231ML2
C. 12ML2\frac{1}{2} ML^221ML2
D. ML2ML^2ML2
✅ Answer: A. 112ML2\frac{1}{12} ML^2121ML2

4. Moment of inertia of a solid sphere about a diameter is:

A. 25MR2\frac{2}{5} MR^252MR2
B. 35MR2\frac{3}{5} MR^253MR2
C. 12MR2\frac{1}{2} MR^221MR2
D. 15MR2\frac{1}{5} MR^251MR2
✅ Answer: A. 25MR2\frac{2}{5} MR^252MR2

5. Which of the following has the highest moment of inertia about its central axis?
A. Solid sphere
B. Hollow sphere
C. Solid cylinder
D. Thin ring
✅ Answer: D. Thin ring

Advanced Level MCQs

6. If the radius of gyration is kkk, then moment of inertia III is given by:
A. I=Mk2I = Mk^2I=Mk2
B. I=M/kI = M/kI=M/k
C. I=MkI = \sqrt{Mk}I=Mk
D. I=MkI = MkI=Mk
✅ Answer: A. I=Mk2I = Mk^2I=Mk2

7. Parallel axis theorem is given by:

A. I=Icm+Md2I = I_{cm} + Md^2I=Icm+Md2
B. I=Icm−Md2I = I_{cm} - Md^2I=Icm−Md2
C. I=Icm/MdI = I_{cm} / MdI=Icm/Md
D. I=Icm+MdI = I_{cm} + MdI=Icm+Md
✅ Answer: A. I=Icm+Md2I = I_{cm} + Md^2I=Icm+Md2

8. A disc and a ring of same mass and radius roll without slipping. Which one has higher kinetic
energy?
A. Disc
B. Ring
C. Both equal
D. Cannot be determined
✅ Answer: B. Ring
(Because ring has higher moment of inertia, so more rotational energy)

9. Which of the following shapes has the minimum moment of inertia for a given mass and size?
A. Ring
B. Solid sphere
C. Hollow sphere
D. Rod
✅ Answer: B. Solid sphere

10. Moment of inertia plays the same role in rotational motion as ___ plays in linear motion.
A. Force
B. Acceleration
C. Mass
D. Velocity
✅ Answer: C. Mass
1. The centroid of a triangle is located at:
A. The intersection of its perpendicular bisectors
B. The intersection of its medians
C. The intersection of its altitudes
D. The midpoint of its base
✅ Answer: B. The intersection of its medians

2. The centroid of a semicircular area lies at a distance of ___ from the base (diameter).
A. 4R3π\frac{4R}{3\pi}3π4R
B. R2\frac{R}{2}2R
C. 3R4\frac{3R}{4}43R
D. RRR
✅ Answer: A. 4R3π\frac{4R}{3\pi}3π4R

3. The coordinates of the centroid of a rectangle of width bbb and height hhh, measured from its
bottom-left corner, are:
A. (0,0)(0, 0)(0,0)
B. (b,h)(b, h)(b,h)
C. (b2,h2)\left( \frac{b}{2}, \frac{h}{2} \right)(2b,2h)
D. (h2,b2)\left( \frac{h}{2}, \frac{b}{2} \right)(2h,2b)
✅ Answer: C. (b2,h2)\left( \frac{b}{2}, \frac{h}{2} \right)(2b,2h)

4. The centroid of a uniform semicircular wire lies:

A. At the center of the circle
B. At a distance 2Rπ\frac{2R}{\pi}π2R from the center
C. At a distance R2\frac{R}{2}2R from the center
D. At a distance 4R3π\frac{4R}{3\pi}3π4R from the base
✅ Answer: B. At a distance 2Rπ\frac{2R}{\pi}π2R from the center

5. Which of the following statements is true about centroid?

A. It always lies inside the body
B. It is the point where the total weight is assumed to act
C. It lies on the axis of symmetry
D. All of the above
✅ Answer: D. All of the above
6. The centroid of a composite shape can be found by:
A. Taking the average of the lengths
B. Using the principle of moments
C. Subtracting areas
D. Rotating the shape
✅ Answer: B. Using the principle of moments

7. The x-coordinate of the centroid xˉ\bar{x}xˉ of multiple areas is given by:

A. xˉ=∑xi\bar{x} = \sum x_ixˉ=∑xi
B. xˉ=∑Ai/xi\bar{x} = \sum A_i / x_ixˉ=∑Ai/xi
C. xˉ=∑Aixi∑Ai\bar{x} = \frac{\sum A_i x_i}{\sum A_i}xˉ=∑Ai∑Aixi
D. xˉ=∑xiAi\bar{x} = \frac{\sum x_i}{A_i}xˉ=Ai∑xi
✅ Answer: C. xˉ=∑Aixi∑Ai\bar{x} = \frac{\sum A_i x_i}{\sum A_i}xˉ=∑Ai∑Aixi

8. For a uniform solid cone, the centroid lies along the axis of the cone at a distance of:
A. h2\frac{h}{2}2h from the base
B. 3h4\frac{3h}{4}43h from the base
C. h3\frac{h}{3}3h from the base
D. h4\frac{h}{4}4h from the vertex
✅ Answer: C. h4\frac{h}{4}4h from the base (or 3h4\frac{3h}{4}43h from the vertex)

9. The centroid of a quarter circle lies at:

A. (4R3π,4R3π)\left( \frac{4R}{3\pi}, \frac{4R}{3\pi} \right)(3π4R,3π4R)
B. (R,R)\left( R, R \right)(R,R)
C. (R2,R2)\left( \frac{R}{2}, \frac{R}{2} \right)(2R,2R)
D. (2Rπ,2Rπ)\left( \frac{2R}{\pi}, \frac{2R}{\pi} \right)(π2R,π2R)
✅ Answer: A. (4R3π,4R3π)\left( \frac{4R}{3\pi}, \frac{4R}{3\pi} \right)(3π4R,3π4R)

10. In a symmetric object, the centroid:

A. Lies along the axis of symmetry
B. Lies outside the object
C. Is undefined
D. Lies at any random point
✅ Answer: A. Lies along the axis of symmetry
1. The bending stress in a beam is directly proportional to:
A. The radius of curvature
B. The area of cross-section
C. The distance from the neutral axis
D. The length of the beam
✅ Answer: C. The distance from the neutral axis

2. The maximum bending stress in a beam occurs at:

A. The neutral axis
B. The topmost fiber only
C. The bottommost fiber only
D. The extreme fibers (top or bottom)
✅ Answer: D. The extreme fibers (top or bottom)

3. The neutral axis of a beam in pure bending is the line where:

A. Maximum stress occurs
B. Shear stress is maximum
C. Bending stress is zero
D. Deflection is maximum
✅ Answer: C. Bending stress is zero

4. The flexural formula (bending equation) is:

A. σ=MyI\sigma = \frac{My}{I}σ=IMy
B. σ=IMy\sigma = \frac{I}{My}σ=MyI
C. M=IσyM = \frac{I}{\sigma y}M=σyI
D. σ=FA\sigma = \frac{F}{A}σ=AF
✅ Answer: A. σ=MyI\sigma = \frac{My}{I}σ=IMy

5. In the bending equation MI=σy=ER\frac{M}{I} = \frac{\sigma}{y} = \frac{E}{R}IM=yσ

=RE, III is:
A. Moment of force
B. Area of the section
C. Moment of inertia
D. Radius of curvature
✅ Answer: C. Moment of inertia

🔴 Advanced Level MCQs

6. Which one of the following is NOT an assumption in the theory of simple bending?
A. Material is homogeneous and isotropic
B. Plane sections before bending remain plane after bending
C. Shear stress is maximum at the neutral axis
D. The beam is initially straight
✅ Answer: C. Shear stress is maximum at the neutral axis
(This is true for shear stress distribution, not an assumption in pure bending theory.)

7. The section modulus ZZZ is defined as:

A. Z=IyZ = \frac{I}{y}Z=yI
B. Z=MIZ = \frac{M}{I}Z=IM
C. Z=yIZ = \frac{y}{I}Z=Iy
D. Z=IMZ = \frac{I}{M}Z=MI
✅ Answer: A. Z=IyZ = \frac{I}{y}Z=yI

8. In a simply supported beam with a point load at the center, the maximum bending moment
occurs:
A. At the supports
B. At the center
C. At quarter-span
D. Uniformly throughout
✅ Answer: B. At the center

9. For a rectangular cross-section b×db \times db×d, the maximum bending stress is:
A. Mbd\frac{M}{bd}bdM
B. 6Mbd2\frac{6M}{bd^2}bd26M
C. 2Mbd\frac{2M}{bd}bd2M
D. 3Mbd\frac{3M}{bd}bd3M
✅ Answer: B. 6Mbd2\frac{6M}{bd^2}bd26M

10. The bending stress in a beam increases when:

A. The moment of inertia increases
B. The applied bending moment decreases
C. The distance from the neutral axis increases
D. The section modulus increases
✅ Answer: C. The distance from the neutral axis increases
1. The method of joints is used to analyze:
A. Beams
B. Frames
C. Trusses
D. Shafts
✅ Answer: C. Trusses

2. In method of joints, the equilibrium of each joint is considered by applying:

A. ∑M=0\sum M = 0∑M=0
B. ∑F=ma\sum F = ma∑F=ma
C. ∑Fx=0\sum F_x = 0∑Fx=0, ∑Fy=0\sum F_y = 0∑Fy=0
D. ∑T=0\sum T = 0∑T=0
✅ Answer: C. ∑Fx=0\sum F_x = 0∑Fx=0, ∑Fy=0\sum F_y = 0∑Fy=0

3. In a pin-jointed truss, each joint is considered to be in:

A. Two-dimensional force system
B. Three-dimensional force system
C. Rotational motion
D. Static indeterminacy
✅ Answer: A. Two-dimensional force system

4. The forces in members of a perfect truss are determined by:

A. Method of moments only
B. Method of joints or method of sections
C. Shear and bending moment
D. Trial and error
✅ Answer: B. Method of joints or method of sections
5. A member of a truss experiences zero force when:
A. It is horizontal
B. It lies between two collinear members with no external load at the joint
C. The joint is at the midpoint
D. The support is fixed
✅ Answer: B. It lies between two collinear members with no external load at the joint

6. The method of joints is most efficient when:

A. All support reactions are unknown
B. Only one member force is required
C. The truss is internally redundant
D. All member forces are to be determined
✅ Answer: D. All member forces are to be determined

7. For a planar truss to be statically determinate, the relation among members mmm, joints jjj,
and reactions rrr is:
A. m=2j+3m = 2j + 3m=2j+3
B. m+r=2jm + r = 2jm+r=2j
C. m=j+rm = j + rm=j+r
D. m+j=2rm + j = 2rm+j=2r
✅ Answer: B. m+r=2jm + r = 2jm+r=2j

8. In a truss, if m+r<2jm + r < 2jm+r<2j, the truss is:

A. Perfect
B. Deficient (unstable)
C. Redundant
D. Indeterminate
✅ Answer: B. Deficient (unstable)

9. A joint in a truss is typically assumed to be:

A. Welded rigidly
B. Fixed support
C. A frictionless pin
D. A roller
✅ Answer: C. A frictionless pin

10. In method of joints, it is generally best to start at a joint:

A. With the most unknowns
B. With one known force
C. With only two unknowns
D. At the top of the truss
✅ Answer: C. With only two unknowns