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Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when centres of three balls are joined. The centre of the mass of system is located at
- a)Horizontal surface
- b)Centre of one of the balls
- c)Line joining centres of any two balls
- d)Point of intersection of the medians
Correct answer is option 'D'. Can you explain this answer?
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Three identical metal balls each of radius r are placed touching each ...
Consider the situation. The centre of mass of the system cannot lie on the horizontal plane because the centre of each metal ball is at a distance equal to its radius above the surface.
Since the system forms an equilateral triangle, the centre of mass should lie at the point of intersection of the medians.
Since the system forms an equilateral triangle, the centre of mass should lie at the point of intersection of the medians.
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Three identical metal balls each of radius r are placed touching each ...
Explanation:
When three identical metal balls are placed touching each other on a horizontal surface, an equilateral triangle is formed. Let's analyze the situation to find the center of mass of the system.
Center of Mass:
The center of mass of a system is the point where the entire mass of the system can be considered to be concentrated. It is the average position of all the particles in the system, weighted according to their masses.
Arrangement of Balls:
In this case, three identical metal balls are placed touching each other on a horizontal surface. When the centers of the three balls are joined, it forms an equilateral triangle.
Equilateral Triangle:
An equilateral triangle is a special type of triangle in which all three sides are equal in length and all three angles are equal to 60 degrees.
Properties of Equilateral Triangle:
1. The medians of an equilateral triangle intersect at a point called the centroid.
2. The centroid divides each median into two segments, with the ratio 2:1.
3. The centroid is also the center of mass of the triangle.
Center of Mass of the System:
Since the three balls are identical and placed symmetrically, the mass is distributed equally among them. Therefore, the center of mass of each ball coincides with the centroid of the equilateral triangle formed by the three balls.
Conclusion:
Hence, the center of mass of the system is located at the point of intersection of the medians of the equilateral triangle formed by the centers of the three balls. Therefore, option D, "Point of intersection of the medians," is the correct answer.
When three identical metal balls are placed touching each other on a horizontal surface, an equilateral triangle is formed. Let's analyze the situation to find the center of mass of the system.
Center of Mass:
The center of mass of a system is the point where the entire mass of the system can be considered to be concentrated. It is the average position of all the particles in the system, weighted according to their masses.
Arrangement of Balls:
In this case, three identical metal balls are placed touching each other on a horizontal surface. When the centers of the three balls are joined, it forms an equilateral triangle.
Equilateral Triangle:
An equilateral triangle is a special type of triangle in which all three sides are equal in length and all three angles are equal to 60 degrees.
Properties of Equilateral Triangle:
1. The medians of an equilateral triangle intersect at a point called the centroid.
2. The centroid divides each median into two segments, with the ratio 2:1.
3. The centroid is also the center of mass of the triangle.
Center of Mass of the System:
Since the three balls are identical and placed symmetrically, the mass is distributed equally among them. Therefore, the center of mass of each ball coincides with the centroid of the equilateral triangle formed by the three balls.
Conclusion:
Hence, the center of mass of the system is located at the point of intersection of the medians of the equilateral triangle formed by the centers of the three balls. Therefore, option D, "Point of intersection of the medians," is the correct answer.
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Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when centres of three balls are joined. The centre of the mass of system is located ata)Horizontal surfaceb)Centre of one of the ballsc)Line joining centres of any two ballsd)Point of intersection of the mediansCorrect answer is option 'D'. Can you explain this answer?
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Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when centres of three balls are joined. The centre of the mass of system is located ata)Horizontal surfaceb)Centre of one of the ballsc)Line joining centres of any two ballsd)Point of intersection of the mediansCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when centres of three balls are joined. The centre of the mass of system is located ata)Horizontal surfaceb)Centre of one of the ballsc)Line joining centres of any two ballsd)Point of intersection of the mediansCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when centres of three balls are joined. The centre of the mass of system is located ata)Horizontal surfaceb)Centre of one of the ballsc)Line joining centres of any two ballsd)Point of intersection of the mediansCorrect answer is option 'D'. Can you explain this answer?.
Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when centres of three balls are joined. The centre of the mass of system is located ata)Horizontal surfaceb)Centre of one of the ballsc)Line joining centres of any two ballsd)Point of intersection of the mediansCorrect answer is option 'D'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when centres of three balls are joined. The centre of the mass of system is located ata)Horizontal surfaceb)Centre of one of the ballsc)Line joining centres of any two ballsd)Point of intersection of the mediansCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when centres of three balls are joined. The centre of the mass of system is located ata)Horizontal surfaceb)Centre of one of the ballsc)Line joining centres of any two ballsd)Point of intersection of the mediansCorrect answer is option 'D'. Can you explain this answer?.
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