Q#1: The area moment of inertia is a measure of:
(A) A shape’s resistance to bending
(B) Mass only
(C) Torque only
(D) Length only
Answer: (A) A shape’s resistance to bending

Q#2: The second moment of area about an axis is given by:
(A)

𝐼

∫
𝑦
2
𝑑
𝐴
I=∫y
2
dA
(B)

𝐼

∫
𝑥
𝑑
𝐴
I=∫xdA
(C)

𝐼

∫
𝑑
𝐴
I=∫dA
(D)

𝐼

∫
𝑥
𝑦
𝑑
𝐴
I=∫xydA
Answer: (A)

𝐼

∫
𝑦
2
𝑑
𝐴
I=∫y
2
dA

(Where y = distance from axis, dA = area element)

Q#3: The moment of inertia of a rectangle about its base is:
(A)

𝐼

𝑏
ℎ
3
3
I=
3
bh
3
​

(B)

𝐼

𝑏
ℎ
2
2
I=
2
bh
2
​

(C)

𝐼

𝑏
ℎ
3
I=bh
3

(D)

𝐼

𝑏
3
ℎ
3
I=
3
b
3
h
​

Answer: (A)

𝐼

𝑏
ℎ
3
3
I=
3
bh
3
​

(b = width, h = height)

Q#4: The moment of inertia of a rectangle about its centroidal axis parallel to base is:
(A)

𝐼

𝑏
ℎ
3
12
I=
12
bh
3
​

(B)

𝐼

𝑏
ℎ
2
2
I=
2
bh
2
​

(C)

𝐼

𝑏
ℎ
3
I=bh
3

(D)

𝐼

𝑏
3
ℎ
3
I=
3
b
3
h
​

Answer: (A)

𝐼

𝑏
ℎ
3
12
I=
12
bh
3
​

Q#5: The moment of inertia of a circle about its centroidal axis is:
(A)

𝐼

𝜋
𝑅
4
4
I=
4
πR
4
​

(B)

𝐼

𝜋
𝑅
3
I=πR
3

(C)

𝐼

𝜋
𝑅
2
I=πR
2

(D)

𝐼

𝜋
𝑅
5
5
I=
5
πR
5
​

Answer: (A)

𝐼

𝜋
𝑅
4
4
I=
4
πR
4
​

Q#6: The moment of inertia of a circle about an axis through the diameter is:
(A)

𝐼

𝜋
𝑅
4
8
I=
8
πR
4
​

(B)

𝐼

𝜋
𝑅
4
4
I=
4
πR
4
​

(C)

𝐼

𝜋
𝑅
3
I=πR
3

(D)

𝐼

𝜋
𝑅
2
I=πR
2

Answer: (A)

𝐼

𝜋
𝑅
4
8
I=
8
πR
4
​

Q#7: The polar moment of inertia of a circle about its center is:
(A)

𝐽

𝜋
𝑅
4
2
J=
2
πR
4
​

(B)

𝐽

𝜋
𝑅
4
4
J=
4
πR
4
​

(C)

𝐽

𝜋
𝑅
3
J=πR
3

(D)

𝐽

𝜋
𝑅
2
J=πR
2

Answer: (A)

𝐽

𝜋
𝑅
4
2
J=
2
πR
4
​

Q#8: The moment of inertia of a thin rod about its centroid perpendicular to length is:
(A)

𝐼

𝐿
3
12
I=
12
L
3
​

(B)

𝐼

𝐿
2
2
I=
2
L
2
​

(C)

𝐼

𝐿
4
4
I=
4
L
4
​

(D)

𝐼

𝐿
3
I=L
3

Answer: (A)

𝐼

𝐿
3
12
I=
12
L
3
​

(L = length, unit width assumed 1)

Q#9: The moment of inertia of a thin rod about its end is:
(A)

𝐼

𝐿
3
3
I=
3
L
3
​

(B)

𝐼

𝐿
3
12
I=
12
L
3
​

(C)

𝐼

𝐿
2
2
I=
2
L
2
​

(D)

𝐼

𝐿
3
I=L
3

Answer: (A)

𝐼

𝐿
3
3
I=
3
L
3
​

Q#10: Parallel axis theorem is used to:
(A) Find the moment of inertia about any axis parallel to centroidal axis
(B) Measure mass
(C) Measure torque only
(D) Calculate stress only
Answer: (A) Find the moment of inertia about any axis parallel to centroidal axis

Q#11: The parallel axis theorem formula is:
(A)

𝐼

𝐼
𝑐
+
𝐴
𝑑
2
I=I
c
​

+Ad
2

(B)

𝐼

𝐼
𝑐
−
𝐴
𝑑
2
I=I
c
​

−Ad
2

(C)

𝐼

𝐼
𝑐
⋅
𝑑
2
I=I
c
​

⋅d
2

(D)

𝐼

𝐴
/
𝑑
2
I=A/d
2

Answer: (A)

𝐼

𝐼
𝑐
+
𝐴
𝑑
2
I=I
c
​

+Ad
2

(I = moment about new axis, Ic = centroidal, A = area, d = distance)

Q#12: The perpendicular axis theorem states:
(A)
𝐼

𝑧

𝐼
𝑥
+
𝐼
𝑦
I
z
​

=I
x
​

+I
y
​

for a lamina in xy-plane
(B)
𝐼

𝑧

𝐼
𝑥
−
𝐼
𝑦
I
z
​

=I
x
​

−I
y
​

(C)
𝐼

𝑧

𝐼
𝑥
⋅
𝐼
𝑦
I
z
​

=I
x
​

⋅I
y
​

(D)
𝐼

𝑧

𝐼
𝑥
/
𝐼
𝑦
I
z
​

=I
x
​

/I
y
​

Answer: (A)
𝐼

𝑧

𝐼
𝑥
+
𝐼
𝑦
I
z
​

=I
x
​

+I
y
​

for a lamina in xy-plane

Q#13: The moment of inertia of a hollow circular section about its centroidal axis is:
(A)

𝐼

𝜋
(
𝑅
𝑜
4
−
𝑅
𝑖
4
)
4
I=
4
π(R
o
4
​

−R
i
4
​

)
​

(B)

𝐼

𝜋
(
𝑅
𝑜
4
+
𝑅
𝑖
4
)
4
I=
4
π(R
o
4
​

+R
i
4
​

)
​

(C)

𝐼

𝜋
(
𝑅
𝑜
2
−
𝑅
𝑖
2
)
I=π(R
o
2
​

−R
i
2
​

)
(D)

𝐼

𝜋
(
𝑅
𝑜
3
−
𝑅
𝑖
3
)
3
I=
3
π(R
o
3
​

−R
i
3
​

)
​

Answer: (A)

𝐼

𝜋
(
𝑅
𝑜
4
−
𝑅
𝑖
4
)
4
I=
4
π(R
o
4
​

−R
i
4
​

)
​

(Ro = outer radius, Ri = inner radius)

Q#14: For a composite area, the moment of inertia can be found by:
(A) Adding or subtracting the moments of individual areas
(B) Measuring edges only
(C) Using torque only
(D) Using mass only
Answer: (A) Adding or subtracting the moments of individual areas

Q#15: The centroidal axis of a section passes through:
(A) The centroid of the section
(B) Edge only
(C) Maximum stress point
(D) Random point
Answer: (A) The centroid of the section

Q#16: The neutral axis of a beam in bending passes through:
(A) The centroid of the cross-section
(B) Base only
(C) Top only
(D) Random point
Answer: (A) The centroid of the cross-section

Q#17: The moment of inertia of a rectangle about an axis along its width at centroid is:
(A)

𝐼

𝑏
ℎ
3
12
I=
12
bh
3
​

(B)

𝐼

𝑏
ℎ
3
3
I=
3
bh
3
​

(C)

𝐼

𝑏
ℎ
3
I=bh
3

(D)

𝐼

ℎ
3
12
I=
12
h
3
​

Answer: (A)

𝐼

𝑏
ℎ
3
12
I=
12
bh
3
​

Q#18: The moment of inertia of a triangle about its base is:
(A)

𝐼

𝑏
ℎ
3
3
I=
3
bh
3
​

(B)

𝐼

𝑏
ℎ
2
2
I=
2
bh
2
​

(C)

𝐼

𝑏
ℎ
3
I=bh
3

(D)

𝐼

𝑏
3
ℎ
3
I=
3
b
3
h
​

Answer: (A)

𝐼

𝑏
ℎ
3
3
I=
3
bh
3
​

Q#19: The centroidal moment of inertia of a circular sector about its base:
(A)

𝐼

𝑅
4
8
I=
8
R
4
​

approx
(B)

𝐼

𝑅
2
I=R
2

(C)

𝐼

𝑅
3
I=R
3

(D)

𝐼

𝑅
4
4
I=
4
R
4
​

Answer: (A)

𝐼

𝑅
4
8
I=
8
R
4
​

approx

Q#20: Area moment of inertia is important in:
(A) Beam bending, shaft design, and structural analysis
(B) Mass measurement only
(C) Torque calculation only
(D) Temperature analysis only
Answer: (A) Beam bending, shaft design, and structural analysis