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If the non-Uniform loading is of the type of parabola then for calculating the radius of gyration?
- a)The net load will not be formed as all the forces will be cancelled
- b)The net force will act the centre of the parabola
- c)The net force will act on the base of the loading horizontally
- d)The net force will act at the centroid of the parabola
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the non-Uniform loading is of the type of parabola then for calcula...
The net force will act at the centroid of the parabola. Whether it be a parabola or the cubic curve the centroid is the only point at which the net force act. Force can’t be acted horizontally if the loading is vertical. Hence whatever be the shape of the loading, the centroid is the point of action of net force. Thus the use of centroid.
Most Upvoted Answer
If the non-Uniform loading is of the type of parabola then for calcula...
The correct answer is option 'D' - The net force will act at the centroid of the parabola.
Explanation:
When a non-uniform load is applied in the form of a parabola, it means that the intensity of the load varies continuously along the length. In such cases, the net force acting on the body can be determined by integrating the individual forces over the entire length of the loading.
The centroid of a parabolic load is the point at which the net force acts. The centroid is the geometric center of the distribution and is given by the formula:
x̄ = ∫(x * w(x)) / ∫w(x)
Here, x̄ represents the position of the centroid, x represents the distance from the reference point, w(x) represents the load intensity at a given position x, and the integrals are taken over the length of the loading.
The radius of gyration is a property that represents the distribution of mass or load about an axis. It is defined as the square root of the ratio of the moment of inertia to the mass or load.
For a parabolic load, the moment of inertia can be calculated as:
I = ∫(x^2 * w(x)) dx
The radius of gyration, k, is then given by:
k = √(I / A)
where A is the total area under the parabolic load.
Since the net force acts at the centroid of the parabola, the moment of inertia is calculated with respect to the centroid. Therefore, the centroid is the reference point for calculating the radius of gyration.
In summary, when the non-uniform loading is in the form of a parabola, the net force acts at the centroid of the parabola. The radius of gyration is then calculated with respect to the centroid.
Explanation:
When a non-uniform load is applied in the form of a parabola, it means that the intensity of the load varies continuously along the length. In such cases, the net force acting on the body can be determined by integrating the individual forces over the entire length of the loading.
The centroid of a parabolic load is the point at which the net force acts. The centroid is the geometric center of the distribution and is given by the formula:
x̄ = ∫(x * w(x)) / ∫w(x)
Here, x̄ represents the position of the centroid, x represents the distance from the reference point, w(x) represents the load intensity at a given position x, and the integrals are taken over the length of the loading.
The radius of gyration is a property that represents the distribution of mass or load about an axis. It is defined as the square root of the ratio of the moment of inertia to the mass or load.
For a parabolic load, the moment of inertia can be calculated as:
I = ∫(x^2 * w(x)) dx
The radius of gyration, k, is then given by:
k = √(I / A)
where A is the total area under the parabolic load.
Since the net force acts at the centroid of the parabola, the moment of inertia is calculated with respect to the centroid. Therefore, the centroid is the reference point for calculating the radius of gyration.
In summary, when the non-uniform loading is in the form of a parabola, the net force acts at the centroid of the parabola. The radius of gyration is then calculated with respect to the centroid.
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If the non-Uniform loading is of the type of parabola then for calculating the radius of gyration?a)The net load will not be formed as all the forces will be cancelledb)The net force will act the centre of the parabolac)The net force will act on the base of the loading horizontallyd)The net force will act at the centroid of the parabolaCorrect answer is option 'D'. Can you explain this answer?
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If the non-Uniform loading is of the type of parabola then for calculating the radius of gyration?a)The net load will not be formed as all the forces will be cancelledb)The net force will act the centre of the parabolac)The net force will act on the base of the loading horizontallyd)The net force will act at the centroid of the parabolaCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If the non-Uniform loading is of the type of parabola then for calculating the radius of gyration?a)The net load will not be formed as all the forces will be cancelledb)The net force will act the centre of the parabolac)The net force will act on the base of the loading horizontallyd)The net force will act at the centroid of the parabolaCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the non-Uniform loading is of the type of parabola then for calculating the radius of gyration?a)The net load will not be formed as all the forces will be cancelledb)The net force will act the centre of the parabolac)The net force will act on the base of the loading horizontallyd)The net force will act at the centroid of the parabolaCorrect answer is option 'D'. Can you explain this answer?.
If the non-Uniform loading is of the type of parabola then for calculating the radius of gyration?a)The net load will not be formed as all the forces will be cancelledb)The net force will act the centre of the parabolac)The net force will act on the base of the loading horizontallyd)The net force will act at the centroid of the parabolaCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If the non-Uniform loading is of the type of parabola then for calculating the radius of gyration?a)The net load will not be formed as all the forces will be cancelledb)The net force will act the centre of the parabolac)The net force will act on the base of the loading horizontallyd)The net force will act at the centroid of the parabolaCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the non-Uniform loading is of the type of parabola then for calculating the radius of gyration?a)The net load will not be formed as all the forces will be cancelledb)The net force will act the centre of the parabolac)The net force will act on the base of the loading horizontallyd)The net force will act at the centroid of the parabolaCorrect answer is option 'D'. Can you explain this answer?.
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