Consider the following statements regarding the centre of gravity and centroid: 1. Centroid of an area does not lie on the axis of symmetry if it exits. 2. Centre of gravity of a body is a point through which the resultant gravitational force acts for any orientation of the body. 3. Centroid is a point in a line plane area volume such that the moment of area about any axis through that point is zero. Which of the above statements are correct?
Analyzing Centre of Gravity and Centroid Statements
The question asks to identify the correct statements about the Centre of Gravity (CG) and Centroid.
Statement Analysis
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Statement 1: Centroid of an area does not lie on the axis of symmetry if it exists.
This statement is incorrect. If an area possesses an axis of symmetry, its centroid must lie on that axis. This is a fundamental property derived from the definition of a centroid.
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Statement 2: Centre of gravity of a body is a point through which the resultant gravitational force acts for any orientation of the body.
This statement is correct. It accurately defines the Centre of Gravity (CG). The weight of an object, which is the resultant gravitational force, always acts through the CG, regardless of how the object is positioned.
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Statement 3: Centroid is a point in a line plane area volume such that the moment of area about any axis through that point is zero.
This statement is correct. It describes the centroid as the geometric center. For any line, plane area, or volume, the first moments about axes passing through the centroid are zero. For an area, this means the moment of area about any axis through the centroid is zero.
Conclusion on Statements
Based on the analysis:
- Statement 1 is incorrect.
- Statement 2 is correct.
- Statement 3 is correct.
Therefore, the correct statements are 2 and 3 only.
The correct option is B.
Important Questions from Centroid
If the centroid of a triangle formed by (7, x), (y, -6) and (9, 10) is (6, 3), then the values of x and y are respectively
What is the area of the triangle formed by these lines?
The centroid of the triangle is at which one of the following points?
If \(\vec a, \vec b, \vec c\) , are the position vectors of the vertices A, B, C respectively of a triangle ABC and G is the centroid of the triangle, then what is \(\overrightarrow{AG}\) equal to ? .
The centroid of the triangle with vertices A(2, -3, 3), B(5, -3, -4) and C(2, -3, -2) is the point
