POLAR & MOMENT OF INERTIA

MULTIPLE CHOICE QUESTIONS

(MCQ) WITH ANSWERS 

MCQ increase the clarity and

understanding. Moment of inertia plays

its role in bending. Higher value resists

bending. Highest value is for I-shaped

cross section. Polar moment of inertia is

important for circular motion as in

shafts. Higher value of polar moment

of inertia reduces shear stress and

distortion.

Fig. Parallel Axis Theorem (I_AB =I_NA +Ah²)

Fig. Perpendicular Axis Theorem (I_zz=J=I_XX+I_YY)

1. Polar moment of inertia is about

1. Neutral axis

2. Centroid axis

3. Neutral fiber

4. None

ANS: (b)

2. Polar moment of inertia is used in

1. Beams

2. Columns

3. Shafts

4. None

ANS: (c )

3. Polar moment of inertia is determined with

1. Parallel axis theorem

2. Perpendicular axis theorem

3. Both parallel & perpendicular axis theorems

4. None

ANS: (b)

4. Polar moment of inertia is given by

1. Firstly          I_xx –I_yy

2. Secondly      I_xx + I_yy

3. Thirdly          I²_xx +I²_yy

4. None

ANS: (b)

5. Polar moment of inertia of a rectangular cross section is

1. (1/12)bh(b²+h²)

2. (1/12)bh(b³+h³)

3. (1/12)(bh)(b⁴+h⁴)

4. None

ANS: (a)

6. Polar moment of inertia of a circular section is

1. (π/64) d³

2. (π/64) d⁴

3. (π/32) d⁴

4. None

ANS: ©

7. Higher polar moment of inertia gives

1. High distortion

2. Less distortion

3. Medium distortion

4. None

ANS: (b)

8. Polar moment of inertia is used in

1. Rectilinear motion

2. Planar motion

3. Circular motion

4. None

ANS: (c )

9. Why is it called polar moment of inertia?

1. It is about a line in the cross-section

2. About a point in the cross-section

3. About a parallel axis in the cross –section

4. None

ANS: (b)

10. Which cross-section is used maximum with polar moment of inertia?

1. Rectangular

2. Square

3. Circular

4. None

ANS: (c )

11. Symbol for polar moment of inertia

1. I

2. J

3. Z

4. None

ANS: (b)

12. Units of polar moment of inertia

1. Firstly      mm³

2. Secondly   mm²

3. Thirdly      mm⁴

4. None

ANS: (c )

13. For a circular section, polar moment of inertia is

1. 4 I_xx

2. 3 I_xx

3. 2 I_xx

4. None

ANS: (c )

14. For a rectangular section, polar moment of inertia is

1. Firstly         2 I_xx

2. Secondly      2 I_yy

3. Thirdly          2 I_zz

4. _None

_ANS: (d)

15. Moment of inertia is for a

1. 3 dimensional body

2. 2 dimensional plain figure

3. 1 dimensional line

4. None

ANS: (b)

16. Symbol for moment of inertia is

1. J

2. I

3. Z

4. None

ANS: (b)

17. Units for moment of inertia is

1. Firstly            mm

2. Secondly       mm²

3. Thirdly          mm³

4. None

ANS: (d)

18. Moment of inertia of a cross-section about xx axis is

1.  Firstly        ∫dA y²

2. Secondly    ∫dA x²

3. Thirdly       ∫dA z²

4. None

ANS: (a)

19. Moment of inertia for a rectangular cross section about xx-axis, width b and depth d is

1. Firstly           I_xx = (1/12) bd⁴

2. Secondly       I_xx = (1/12) bd²

3. Thirdly            I_xx = (1/12) bd³

4. None

ANS: ©

20. Moment of inertia for a square cross section, each side is ‘a’

1. Firstly             I_xx =I_yy =  (1/12) a⁴

2. Secondly         I_xx =I_yy =  (1/12) a³

3. Thirdly             I_xx =I_yy =  (1/12) a²

4. None

ANS: (a)

21. Moment of inertia for a circular solid cross section

1. Firstly            I_xx =I_yy =  (π/64) d³

2. Secondly        I_xx =I_yy =  (π/64) d²

3. Thirdly            I_xx =I_yy =  (π/64) d⁴

4.  (d)None

ANS: (c )

22. Moment of inertia for a circular hollow cross section

1. (a) I_xx =I_yy =  (π/32)[ d_o⁴ – d_i⁴ ]

2. (b) I_xx =I_yy =  (π/64)[ d_o⁴ – d_i⁴ ]

3. © I_xx =I_yy =  (π/16)[ d_o⁴ – d_i⁴ ]

4. (d)None

ANS: (b)

23. Use of moment of inertia is in

1. Torsion

2. Bending

3. Tension

4. None

ANS: (b)

24. Larger value of moment of inertia reduces

1. Distortion

2. Deformation

3. Both distortion & deformation

4. None

ANS: (b)

 25. Which is best section with same value of cross sectional area?

1. Rectangular

2. Circular

3. Elliptical

4. None

ANS: (d)

26. Which is best section with same value of cross sectional area?

1. Rectangular

2. Circular

3. I-section

4. None

ANS: (c)

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