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Side of an equilateral triangle is L .Three point masses, each of magnitude M , are placed at three vertices of the triangle .Moment of inertia of the system about one side of the triangle as axis is given by . Ans: 3/4 ML^2?
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Side of an equilateral triangle is L .Three point masses, each of magn...
Problem:
Side of an equilateral triangle is L. Three point masses, each of magnitude M, are placed at three vertices of the triangle. Moment of inertia of the system about one side of the triangle as axis is given by.
Answer:
Given:
- Side of the equilateral triangle = L
- Mass of each point mass = M
To find:
Moment of inertia of the system about one side of the triangle as axis.
Explanation:
To find the moment of inertia of the system, we can consider each point mass separately and then sum up their individual moments of inertia.
Moment of Inertia of a Single Point Mass:
The moment of inertia of a point mass M about an axis passing through its center of mass and perpendicular to the plane of motion is given by the formula:
I = MR^2
Calculating the Moment of Inertia for the System:
Since each point mass is located at one of the vertices of the equilateral triangle, the distances between the point masses and the axis of rotation will be equal to the side length L of the triangle.
The moment of inertia for each point mass will be given by:
I = ML^2
Since there are three point masses in the system, the total moment of inertia of the system will be the sum of the individual moments of inertia:
I_total = 3(ML^2)
Simplifying the expression:
I_total = 3ML^2
Final Answer:
The moment of inertia of the system about one side of the triangle as axis is 3/4 ML^2.
Side of an equilateral triangle is L. Three point masses, each of magnitude M, are placed at three vertices of the triangle. Moment of inertia of the system about one side of the triangle as axis is given by.
Answer:
Given:
- Side of the equilateral triangle = L
- Mass of each point mass = M
To find:
Moment of inertia of the system about one side of the triangle as axis.
Explanation:
To find the moment of inertia of the system, we can consider each point mass separately and then sum up their individual moments of inertia.
Moment of Inertia of a Single Point Mass:
The moment of inertia of a point mass M about an axis passing through its center of mass and perpendicular to the plane of motion is given by the formula:
I = MR^2
Calculating the Moment of Inertia for the System:
Since each point mass is located at one of the vertices of the equilateral triangle, the distances between the point masses and the axis of rotation will be equal to the side length L of the triangle.
The moment of inertia for each point mass will be given by:
I = ML^2
Since there are three point masses in the system, the total moment of inertia of the system will be the sum of the individual moments of inertia:
I_total = 3(ML^2)
Simplifying the expression:
I_total = 3ML^2
Final Answer:
The moment of inertia of the system about one side of the triangle as axis is 3/4 ML^2.
Community Answer
Side of an equilateral triangle is L .Three point masses, each of magn...
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Side of an equilateral triangle is L .Three point masses, each of magnitude M , are placed at three vertices of the triangle .Moment of inertia of the system about one side of the triangle as axis is given by . Ans: 3/4 ML^2?
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Side of an equilateral triangle is L .Three point masses, each of magnitude M , are placed at three vertices of the triangle .Moment of inertia of the system about one side of the triangle as axis is given by . Ans: 3/4 ML^2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Side of an equilateral triangle is L .Three point masses, each of magnitude M , are placed at three vertices of the triangle .Moment of inertia of the system about one side of the triangle as axis is given by . Ans: 3/4 ML^2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Side of an equilateral triangle is L .Three point masses, each of magnitude M , are placed at three vertices of the triangle .Moment of inertia of the system about one side of the triangle as axis is given by . Ans: 3/4 ML^2?.
Side of an equilateral triangle is L .Three point masses, each of magnitude M , are placed at three vertices of the triangle .Moment of inertia of the system about one side of the triangle as axis is given by . Ans: 3/4 ML^2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Side of an equilateral triangle is L .Three point masses, each of magnitude M , are placed at three vertices of the triangle .Moment of inertia of the system about one side of the triangle as axis is given by . Ans: 3/4 ML^2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Side of an equilateral triangle is L .Three point masses, each of magnitude M , are placed at three vertices of the triangle .Moment of inertia of the system about one side of the triangle as axis is given by . Ans: 3/4 ML^2?.
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