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Circular plate of diameter d, and a square plate of edge d are kept flat such that their centres are separated by a distance R as shown in the figure. The density of the material and the thickness of both objects are same. The line joining the two centres is normal to one pair of the edges of the square. If thecentre of mass (C) of this system lies at the midpoint of the edge as shown, then what is the distance between the two centres?
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Circular plate of diameter d, and a square plate of edge d are kept fl...
Given Information:
- The diameter of the circular plate is 'd'.
- The edge of the square plate is also 'd'.
- The centers of both plates are separated by a distance 'R'.
- The density and thickness of both objects are the same.
- The line joining the two centers is normal to one pair of the edges of the square.
- The center of mass (C) of the system lies at the midpoint of the edge.
To Find:
The distance between the two centers.
Explanation:
Step 1: Identifying the Symmetry
- The given figure shows that the square plate and the circular plate have a symmetry axis of rotation.
- The line joining the two centers is normal to one pair of the edges of the square.
- This means that the system has a rotational symmetry of 180 degrees about the line joining the centers.
Step 2: Center of Mass (C)
- The center of mass of the system lies at the midpoint of the edge of the square.
- This implies that the center of mass lies on the line joining the centers of the circular and square plates.
- Let's call the distance between the center of mass and the center of the circular plate as 'x'.
Step 3: Symmetry Analysis
- The system has a rotational symmetry of 180 degrees.
- The center of mass (C) is equidistant from the centers of both plates.
- Therefore, the distance between the center of the circular plate and the center of mass is also 'x'.
- The distance between the center of the square plate and the center of mass is also 'x'.
Step 4: Distance Between the Centers
- The distance between the two centers is the sum of the distances between each center and the center of mass.
- Hence, the distance between the two centers is 2x.
Step 5: Using Geometric Analysis to Find x
- The line joining the two centers is normal to one pair of the edges of the square.
- This implies that the distance between the center of the square plate and the center of mass is half the length of the edge of the square.
- Therefore, x = d/2.
Step 6: Final Answer
- The distance between the two centers is 2x = 2 * (d/2) = d.
Answer:
- The distance between the two centers is 'd'.
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Circular plate of diameter d, and a square plate of edge d are kept flat such that their centres are separated by a distance R as shown in the figure. The density of the material and the thickness of both objects are same. The line joining the two centres is normal to one pair of the edges of the square. If thecentre of mass (C) of this system lies at the midpoint of the edge as shown, then what is the distance between the two centres?
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Circular plate of diameter d, and a square plate of edge d are kept flat such that their centres are separated by a distance R as shown in the figure. The density of the material and the thickness of both objects are same. The line joining the two centres is normal to one pair of the edges of the square. If thecentre of mass (C) of this system lies at the midpoint of the edge as shown, then what is the distance between the two centres? 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 Circular plate of diameter d, and a square plate of edge d are kept flat such that their centres are separated by a distance R as shown in the figure. The density of the material and the thickness of both objects are same. The line joining the two centres is normal to one pair of the edges of the square. If thecentre of mass (C) of this system lies at the midpoint of the edge as shown, then what is the distance between the two centres? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Circular plate of diameter d, and a square plate of edge d are kept flat such that their centres are separated by a distance R as shown in the figure. The density of the material and the thickness of both objects are same. The line joining the two centres is normal to one pair of the edges of the square. If thecentre of mass (C) of this system lies at the midpoint of the edge as shown, then what is the distance between the two centres?.
Circular plate of diameter d, and a square plate of edge d are kept flat such that their centres are separated by a distance R as shown in the figure. The density of the material and the thickness of both objects are same. The line joining the two centres is normal to one pair of the edges of the square. If thecentre of mass (C) of this system lies at the midpoint of the edge as shown, then what is the distance between the two centres? 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 Circular plate of diameter d, and a square plate of edge d are kept flat such that their centres are separated by a distance R as shown in the figure. The density of the material and the thickness of both objects are same. The line joining the two centres is normal to one pair of the edges of the square. If thecentre of mass (C) of this system lies at the midpoint of the edge as shown, then what is the distance between the two centres? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Circular plate of diameter d, and a square plate of edge d are kept flat such that their centres are separated by a distance R as shown in the figure. The density of the material and the thickness of both objects are same. The line joining the two centres is normal to one pair of the edges of the square. If thecentre of mass (C) of this system lies at the midpoint of the edge as shown, then what is the distance between the two centres?.
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