Mechanical Engineering Principles

FIRST AND SECOND MOMENT OF AREAS 101

(a) 16 cm^4 (b) 4 cm^4

(c) 36 cm^4 (d) 144 cm^4

G

60 mm

15 mm

20 mmG

X X

Figure 7.41

3. The second moment of area about
   axis XX of the rectangle shown in
   Figure 7.41 is:
   (a) 111 cm^4 (b) 31 cm^4
   (c) 63 cm^4 (d) 79 cm^4


4. The radius of gyration about axis
   GG of the rectangle shown in
   Figure 7.41 is:

(a) 5.77 mm (b) 17.3 mm

(c) 11.55 mm (d) 34.64 mm

5. The radius of gyration about axisXXof
   the rectangle shown in Figure 7.41 is:

(a) 30.41 mm (b) 25.66 mm

(c) 16.07 mm (d) 22.91 mm

The circumference of a circle is 15.71 mm.
Use this fact in questions 6 to 8.

6. The second moment of area of the cir-
   cle about an axis coinciding with its
   diameter is:
   (a) 490.9 mm^4 (b) 61.36 mm^4
   (c) 30.69 mm^4 (d) 981.7 mm^4
   7. The second moment of area of the circle
   about a tangent is:

(a) 153.4 mm^4 (b) 9.59 mm^4

(c) 2454 mm^4 (d) 19.17 mm^4

8. The polar second moment of area of the
   circle is:

(a) 3.84 mm^4 (b) 981.7 mm^4

(c) 61.36 mm^4 (d) 30.68 mm^4

9. The second moment of area about axis
   XX of the triangle ABC shown in
   Figure 7.42 is:

(a) 24 cm^4 (b) 10.67 cm^4

(c) 310.67 cm^4 (d) 324 cm^4

C B

G G

X X

A

6.0 cm

3.0 cm

4.0 cm

Figure 7.42

10. The radius of gyration about axisGGof
    the triangle shown in Figure 7.42 is:

(a) 1.41 cm (b) 2 cm

(c) 2.45 cm (d) 4.24 cm