This set of Strength of Materials Multiple Choice Questions & Answers (MCQs) focuses on “Moment of Inertia”.

1. The axis about which moment of area is taken is known as ____________

a) Axis of area

b) Axis of moment

c) Axis of reference

d) Axis of rotation

View Answer

Explanation: The axis of reference is the axis about which moment of area is taken. Most of the times it is either the standard x or y axis or the centeroidal axis.

2. Point, where the total volume of the body is assumed to be concentrated is ____________

a) Center of area

b) Centroid of volume

c) Centroid of mass

d) All of the mentioned

View Answer

Explanation: The centroid of the volume is the point where total volume is assumed to be concentrated. It is the geometric centre of a body. If the density is uniform throughout the body, then the center of mass and center of gravity correspond to the centroid of volume. The definition of the centroid of volume is written in terms of ratios of integrals over the volume of the body.

3. What is MOI?

a) ml^{2}

b) mal

c) ar^{2}

d) None of the mentioned

View Answer

Explanation: The formula of the moment of inertia is, MOI = ar

^{2}where

M = mass, a = area, l = length, r = distance.

4. What is the formula of radius of gyration?

a) k^{2} = I/A

b) k^{2} = I^{2}/A

c) k^{2} = I^{2}/A^{2}

d) k^{2} = (I/A)^{1/2}

View Answer

Explanation: The radius of gyration of a body about an axis is a distance such that its square multiplied by the area gives moment of inertia of the area about the given axis. The formula of radius of gyration is given as k

^{2}= I/A.

5. What is the formula of theorem of perpendicular axis?

a) I_{zz} = I_{xx} – I_{yy}

b) I_{zz} = I_{xx} + Ah^{2}

c) I_{zz} – I_{xx} = I_{yy}

d) None of the mentioned

View Answer

Explanation: Theorem of perpendicular axis stares that if I

_{XX}and I

_{YY}be the moment of inertia of a plane section about two mutually perpendicular axis X-X and Y-Y in the plane of the section then the moment of inertia of the section I

_{ZZ}about the axis Z-Z, perpendicular to the plane and passing through the intersection of X-X and Y-Y is given by the formula

I

_{zz}– I

_{xx}= I

_{yy}.

6. What is the formula of theorem of parallel axis?

a) I_{AD} = I_{G} + Ah

b) I_{AB} = Ah^{2} + IG

c) I_{AB} = I_{G} – Ah^{2}

d) I_{AB} = I_{G} + I_{xx}

View Answer

Explanation: The theorem of parallel axis states that if the moment of inertia of a plane area about an axis in the plane of area theough the C.G. of the plane area be represented by IG, then the moment of the inertia of the given plane area about a parallel axis AB in the plane of area at a distance h from the C.G. is given by the formula

I

_{AB}= Ah

^{2}+ I

_{G}.

7. What is the unit of radius of gyration?

a) m^{4}

b) m

c) N

d) m^{2}

View Answer

Explanation: The radius of gyration = (length

^{4}/length

^{2})1/2 = length

So its unit will be m.

8. What will be the the radius of gyration of a circular plate of diameter 10cm?

a) 1.5cm

b) 2.0cm

c) 2.5cm

d) 3cm

View Answer

Explanation: The moment of inertia of a circle, I = πD

^{4}/64 = 491.07 cm

^{4}

The area of circle = 78.57 cm,

Radius of gyration = (I/A)

^{1/2}= 2.5 cm.

**Sanfoundry Global Education & Learning Series – Strength of Materials. **

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