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Three identical spheres each of mass 1kg are placed touching each other with their centres on a straight line .Their centre is marked as P,Q,R resp. The distance of centre of mass of the system from P is?
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Problem Statement:
Three identical spheres, each of mass 1kg, are placed touching each other with their centers on a straight line. Their centers are marked as P, Q, and R, respectively. The task is to determine the distance of the center of mass of the system from point P.
Solution:
To find the distance of the center of mass of the system from point P, we need to first calculate the individual distances of each sphere's center of mass from point P and then take the average.
Step 1: Finding the distance of the center of mass of each sphere from point P:
Since the spheres are identical and have the same mass, the center of mass of each sphere will be located at its geometric center. Let's assume the radius of each sphere to be r.
1. The center of mass of sphere P is at point P itself, so the distance is 0.
2. The center of mass of sphere Q will be at a distance of r from point P.
3. The center of mass of sphere R will be at a distance of 2r from point P.
Step 2: Calculating the average distance:
To find the average distance, we need to add up the distances of the center of mass of each sphere from point P and then divide by the total number of spheres (which is 3 in this case).
Average distance = (0 + r + 2r) / 3
Simplifying the expression, we get:
Average distance = (3r) / 3
Therefore, the average distance of the center of mass of the system from point P is equal to the radius of each sphere, which is r.
Conclusion:
The distance of the center of mass of the system from point P is equal to the radius of each sphere.
Three identical spheres, each of mass 1kg, are placed touching each other with their centers on a straight line. Their centers are marked as P, Q, and R, respectively. The task is to determine the distance of the center of mass of the system from point P.
Solution:
To find the distance of the center of mass of the system from point P, we need to first calculate the individual distances of each sphere's center of mass from point P and then take the average.
Step 1: Finding the distance of the center of mass of each sphere from point P:
Since the spheres are identical and have the same mass, the center of mass of each sphere will be located at its geometric center. Let's assume the radius of each sphere to be r.
1. The center of mass of sphere P is at point P itself, so the distance is 0.
2. The center of mass of sphere Q will be at a distance of r from point P.
3. The center of mass of sphere R will be at a distance of 2r from point P.
Step 2: Calculating the average distance:
To find the average distance, we need to add up the distances of the center of mass of each sphere from point P and then divide by the total number of spheres (which is 3 in this case).
Average distance = (0 + r + 2r) / 3
Simplifying the expression, we get:
Average distance = (3r) / 3
Therefore, the average distance of the center of mass of the system from point P is equal to the radius of each sphere, which is r.
Conclusion:
The distance of the center of mass of the system from point P is equal to the radius of each sphere.
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Three identical spheres each of mass 1kg are placed touching each other with their centres on a straight line .Their centre is marked as P,Q,R resp. The distance of centre of mass of the system from P is?
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Three identical spheres each of mass 1kg are placed touching each other with their centres on a straight line .Their centre is marked as P,Q,R resp. The distance of centre of mass of the system from P is? 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 spheres each of mass 1kg are placed touching each other with their centres on a straight line .Their centre is marked as P,Q,R resp. The distance of centre of mass of the system from P is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical spheres each of mass 1kg are placed touching each other with their centres on a straight line .Their centre is marked as P,Q,R resp. The distance of centre of mass of the system from P is?.
Three identical spheres each of mass 1kg are placed touching each other with their centres on a straight line .Their centre is marked as P,Q,R resp. The distance of centre of mass of the system from P is? 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 spheres each of mass 1kg are placed touching each other with their centres on a straight line .Their centre is marked as P,Q,R resp. The distance of centre of mass of the system from P is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical spheres each of mass 1kg are placed touching each other with their centres on a straight line .Their centre is marked as P,Q,R resp. The distance of centre of mass of the system from P is?.
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