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

Question-AnswerCategory: Engineering MechanicsA thin steel wire of uniform cross section is bent into the shape shown. Locate its center of gravity.

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 .