# Strength of Materials Questions and Answers – Moment of Inertia of Section

This set of Strength of Materials Problems focuses on “Moment of Inertia of Section”.

1. What is the moment of inertia of a circular section?
a) πD4/64
b) πD3/32
c) πD3/64
d) πD4/32

Explanation: The moment of inertia of a circular section is πD4/64.

2. What is the moment of inertia of a rectangular section about an horizontal axis through C.G?
a) bd3/6
b) bd2/12
c) b2d2/12
d) bd3/12

Explanation: The moment of inertia of a rectangular section about an horizontal axis through C.G is bd3/12.

3. What is the moment of inertia of a rectangular section about an horizontal axis passing through base?
a) bd3/12
b) bd3/6
c) bd3/3
d) bd2/3

Explanation: The moment of inertia of a rectangular section about an horizontal axis passing through base is bd3/3.

4. What is the moment of inertia of a triangular section about the base?
a) bh2/12
b) bh3/12
c) bh3/6
d) bh2/6

Explanation: The moment of inertia of a triangular section about the base is bh3/12.

5. What is the moment of inertia of a triangular section about an axis passing through C.G. and parallel to the base?
a) bh3/12
b) bh3/24
c) bh3/36
d) bh3/6

Explanation: The moment of inertia of a triangular section about an axis passing through C.G. and parallel to the base is bh3/36.
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6. What will be the moment of inertia of a circle in cm4 of diameter is 10cm?
a) a340
b) 410
c) 460
d) 490

Explanation: The moment of inertia of a circle is = πD4/64
= 491.07 cm4.

7. What will be the moment of inertia of the given rectangle about an horizontal axis passing through the base?

a) 1500 mm4
b) 1650 mm4
c) 1666 mm4
d) 1782 mm4

Explanation: The moment of inertia of a rectangular section about an horizontal axis passing through base = bd3/3
= 5x10x10x10/3
= 1666.66 mm4.

8. What will be the moment of inertia of the given rectangular section about an horizontal axis through C.G.?

a) 350 mm4
b) 379mm4
c) 416mm4
d) 500mm4

Explanation: The moment of inertia of a rectangular section about an horizontal axis through C.G = bd3/12
= 5x10x10x10/12
= 416.67 mm4.

9. What will be the moment of inertia of the given triangle about the base?

a) 20.33 mm4
b) 21.33 mm4
c) 24.33 mm4
d) 22.33 mm4

Explanation: The moment of inertia of a triangular section about the base = bh3/12.
= 4x4x4x4/12
= 21.33 mm4.

10. What will be the moment of inertia of the given triangle about an axis passing through C.G and parallel to base?

a) 6.1 mm4
b) 7.1 mm4
c) 8.1 mm4
d) 7.56 mm4

Explanation: The moment of inertia of a triangular section about an axis passing through C.G. and parallel to the base = bh3/36.
= 4x4x4x4/36
= 7.11 mm4.

11. What will be the difference between MOI of two triangle sections is in 1st, MOI is taken about its base and in 2nd MOI is taken about its centroid?
a) bh3/12
b) bh3/18
c) bh3/36
d) bh3/24

Explanation: The moment of inertia of a triangular section about the base is bh3/12
The moment of inertia of a triangular section about an axis passing through C.G. is bh3/36
So the difference = bh3/12 – bh3/36 = bh3/18.

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