Answer to Question #279903 in Classical Mechanics for alfi

Question

 Find the center of mass of each of the following: (a) Athin wire bent into the form of a three-sided, block-shaped "Ll"with each segment of equal length b (b) A quadrant of a uniform circular lamina of radius b (c) The area bounded by parabola y =x2/b and the line y =b (d) The volume bounded by paraboloid of revolution z = (x2 +y2)/b and the plane z = b 

Answer 1

a)

$x=\frac b2,~y=\frac b3.$

b)

$x=0,~y=0.$

c)

$x=0,~y=\frac {b\sqrt 2}2.$

d)

$x=0,~y=0,~z=\frac{b\sqrt 3}2.$