chapter

Assignment 10

Pages 1

Fig. A10.1. The section of the groove is a semicircle of diameter 50 mm. Given that the centroid of a semicircle from its base is

4r 3π

, use the theorem of Pappus to determine the volume of material removed, in cm3, correct to 3 significant figures. (8)

8. A circular door is hinged so that it turns about a tangent. If its diameter is 1.0 m find its second moment of area and radius of gyration about the hinge. (5)

9. Determine the following integrals:

(a) ∫

5(6t + 5)7 dt (b) ∫ 3 ln x

x dx

(c) ∫ 2√(2θ − 1) dθ (9)

10. Evaluate the following definite integrals:

(a) ∫ π

0 2 sin

( 2t + π

) dt (b)

(10)