integration
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390 INTEGRAL CALCULUS<br />
in Fig. 38.33. (In Fig. 38.33(b), the circular<br />
area is removed.) ⎡<br />
⎣ I AA = 4224 cm 4 ⎤<br />
,<br />
I BB = 6718 cm 4 , ⎦<br />
I cc = 37300 cm 4<br />
Figure 38.31<br />
6. Calculate the radius of gyration of a rectangular<br />
door 2.0 m high by 1.5 m wide about a<br />
vertical axis through its hinge.<br />
[0.866 m]<br />
7. A circular door of a boiler is hinged so that<br />
it turns about a tangent. If its diameter is<br />
1.0 m, determine its second moment of area<br />
and radius of gyration about the hinge.<br />
[0.245 m 4 , 0.559 m]<br />
8. A circular cover, centre 0, has a radius of<br />
12.0 cm. A hole of radius 4.0 cm and centre<br />
X, where OX = 6.0 cm, is cut in the cover.<br />
Determine the second moment of area and<br />
the radius of gyration of the remainder about<br />
a diameter through 0 perpendicular to OX.<br />
[14280 cm 4 , 5.96 cm]<br />
Figure 38.33<br />
11. Find the second moment of area and radius<br />
of gyration about the axis XX for the beam<br />
section shown in Fig. 38.34. [<br />
1350 cm 4 ,<br />
]<br />
5.67 cm<br />
9. For the sections shown in Fig. 38.32, find<br />
the second moment of area and the radius of<br />
gyration about axis [ XX.<br />
(a) 12190 mm 4 ]<br />
,10.9mm<br />
(b) 549.5cm 4 ,4.18 cm<br />
Figure 38.34<br />
Figure 38.32<br />
10. Determine the second moments of areas<br />
about the given axes for the shapes shown
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