If the given figure is straight line one dimensional, then centroid of such kind of figures lies at a distance L/2 from reference axis. As shown below:
Centroid of straight line
Examples
- A steel rod has total length of 50 cm. student want to stable it on a vertical pointed edge. For this it is required to find the point of rod where load balanced out and that point is known as center of gravity (centroid) of rod.
Solution:
centroid (center of gravity) of straight line lies at a distance L/2.
\(\bar{X}\) = L/2 = 50/2 = 25 cm.
Hence, center of gravity of a steel rod lies at a distance of 25 cm from x-axis.
2. Student of Civil Engineers want to know the centroid of plane table survey instrument. They measured 2.5 ft. distance between two legs of instrument.
Solution:
Centroid lies at a distance of L/2 = 2.5/2 = 1.25 ft.
3. A 100 ft. long gas pipe is need to transferred from store to ship with the help of crane. find the point where the pipe is picked up so that the load on both side will remain same.
Solution:
It is very simple to find the point of straight pipe where load balanced on both sides. Simply find the Centroid of 100 ft.
Centroid of 100 ft. lies at a distance L/2 = 50 ft.
