GME asked 1 year ago
A thin steel wire of uniform cross section is bent into the shape shown. Locate its center of gravity.
Sazid Ahmad answered 1 year ago
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 
.