Question
Download Solution PDFWhat will be the location of the centroid of a quadrant circle, (where 'r' is radius of the circle)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The centroid, C, is a point defining the geometric centre of an object.
The centroid coincides with the centre of mass or the centre of gravity only if the material of the body is homogenous (density or specific weight is constant throughout the body).
|
Shape |
Figure |
Area |
\(\bar x\) |
\(\bar y\) |
|
Semicircle
|
|
\(\frac{{\pi {R^2}}}{2}\) |
\(\frac{{4R}}{{3\pi }}\) |
0 |
|
Semicircle |
|
\(\frac{{\pi {R^2}}}{2}\) |
0 |
\(\frac{{4R}}{{3\pi }}\) |
|
Quadrant |
|
\(\frac{{\pi {R^2}}}{4}\) |
\(\frac{{4R}}{{3\pi }}\) |
\(\frac{{4R}}{{3\pi }}\) |
|
Semi – elliptical Area |
|
\(\frac{{\pi ab}}{2}\) |
0 |
\(\frac{{4b}}{{3\pi }}\) |
|
Parabola |
|
\(\frac{1}{3}bh\) |
\(\frac{{3b}}{4}\) |
\(\frac{{3h}}{{10}}\) |
For a given semi-circular area of diameter d
We can find the centroid from the above table as \(2d\over 3π\).
Last updated on May 9, 2025
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