A thin steel wire of uniform cross section is bent into the shape shown. Locate its center of gravity.

Step: 1

Draw the free body diagram of line segments.

Step: 2

The lengths and coordinate of the centroid of each of these components are entered in table below.

Line segment

Length

OA

0

0.5

0

AB

1.2

0.5

0

BC

0

CO

2.4

0

0

1.2

Step: 3

Calculate the first moment of its length with respect to the yz plane:

Calculate the first moment of its length with respect to the xz plane:

Calculate the first moment of its length with respect to the xy plane:

Step: 4

Calculate the x – coordinate of the body:

Substitute, for, for

Therefore, the x – coordinate of the centre of gravity is .

Step: 5

Calculate the y – coordinate of the body:

Substitute, for, for

Therefore, the y – coordinate of the centre of gravity is .

Step: 6

Calculate the z – coordinate of the body:

Substitute, for, for

Therefore, the z – coordinate of the centre of gravity is .