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four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere
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four identical spheres of radius 10cm and mass 10kg are placed on a ho...
Calculating the Center of Mass of the Spheres
To find the distance of the center of mass from the center of one of the spheres, we first need to determine the position of the center of mass of the system of four spheres.
- Since the spheres are identical and symmetrically placed, the center of mass of the system will lie at the center of the square formed by the spheres.
- The center of mass of the square formed by the spheres can be found by taking the average of the x-coordinates and y-coordinates of the centers of the spheres.
- The x-coordinate of the center of mass will be the average of the x-coordinates of the four spheres, which is 0 since the spheres are symmetrically placed.
- The y-coordinate of the center of mass will be the average of the y-coordinates of the four spheres, which is also 0.
- Therefore, the center of mass of the system of four spheres lies at the center of the square formed by the spheres.
Calculating the Distance of the Center of Mass from the Center of One Sphere
- The distance of the center of mass from the center of one of the spheres can be calculated using the distance formula.
- Since the center of mass lies at the center of the square formed by the spheres, the distance of the center of mass from the center of one of the spheres will be half the diagonal of the square.
- The diagonal of the square formed by the spheres can be calculated using the Pythagorean theorem, which gives us a diagonal of 28.28 cm.
- Therefore, the distance of the center of mass from the center of one of the spheres is half of the diagonal, which is 14.14 cm.
In conclusion, the center of mass of the system of four spheres lies at the center of the square formed by the spheres, and the distance of the center of mass from the center of one sphere is 14.14 cm.
To find the distance of the center of mass from the center of one of the spheres, we first need to determine the position of the center of mass of the system of four spheres.
- Since the spheres are identical and symmetrically placed, the center of mass of the system will lie at the center of the square formed by the spheres.
- The center of mass of the square formed by the spheres can be found by taking the average of the x-coordinates and y-coordinates of the centers of the spheres.
- The x-coordinate of the center of mass will be the average of the x-coordinates of the four spheres, which is 0 since the spheres are symmetrically placed.
- The y-coordinate of the center of mass will be the average of the y-coordinates of the four spheres, which is also 0.
- Therefore, the center of mass of the system of four spheres lies at the center of the square formed by the spheres.
Calculating the Distance of the Center of Mass from the Center of One Sphere
- The distance of the center of mass from the center of one of the spheres can be calculated using the distance formula.
- Since the center of mass lies at the center of the square formed by the spheres, the distance of the center of mass from the center of one of the spheres will be half the diagonal of the square.
- The diagonal of the square formed by the spheres can be calculated using the Pythagorean theorem, which gives us a diagonal of 28.28 cm.
- Therefore, the distance of the center of mass from the center of one of the spheres is half of the diagonal, which is 14.14 cm.
In conclusion, the center of mass of the system of four spheres lies at the center of the square formed by the spheres, and the distance of the center of mass from the center of one sphere is 14.14 cm.
Community Answer
four identical spheres of radius 10cm and mass 10kg are placed on a ho...
14.32m
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four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere
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four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere.
four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere.
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