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A Square Plate of Edge a and a circular disc of same diameter are placed touching each other at the midpoint of the edge of the plate as shown in the figure if the mass per unit of the two plates are same then find the distance of centre of mass of the system from the centre of the disc?
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A Square Plate of Edge a and a circular disc of same diameter are plac...
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A Square Plate of Edge a and a circular disc of same diameter are plac...
Understanding the System
To find the center of mass of the system comprising a square plate and a circular disc, we first need to establish their dimensions and properties.
- The square plate has an edge length of "a".
- The circular disc has a diameter equal to the edge of the plate, which is also "a".
Mass Calculation
Given that the mass per unit area of both the square plate and the circular disc is the same, we can denote it as "σ".
- Area of the square plate = a²
- Area of the circular disc = π(a/2)² = πa²/4
The masses of the two shapes can be calculated as follows:
- Mass of the square plate (M1) = σ * a²
- Mass of the circular disc (M2) = σ * (πa²/4)
Positioning the Shapes
- The center of the square plate is at (a/2, a/2) in a Cartesian coordinate system.
- The center of the circular disc is at (0, a/4) since it is touching the edge of the square plate at its midpoint.
Finding the Center of Mass
The coordinates of the center of mass (COM) can be found using the formula:
COM = (M1 * x1 + M2 * x2) / (M1 + M2), (M1 * y1 + M2 * y2) / (M1 + M2)
Where:
- (x1, y1) = coordinates of the square plate's center
- (x2, y2) = coordinates of the circular disc's center
Substituting the values, we can determine the center of mass relative to the disc's center.
Final Calculation
After substituting the respective masses and coordinates into the formula, we can arrive at the distance from the center of the disc to the center of mass of the system.
This distance gives a clear understanding of the distribution of mass and how the two shapes interact in this combined system.
To find the center of mass of the system comprising a square plate and a circular disc, we first need to establish their dimensions and properties.
- The square plate has an edge length of "a".
- The circular disc has a diameter equal to the edge of the plate, which is also "a".
Mass Calculation
Given that the mass per unit area of both the square plate and the circular disc is the same, we can denote it as "σ".
- Area of the square plate = a²
- Area of the circular disc = π(a/2)² = πa²/4
The masses of the two shapes can be calculated as follows:
- Mass of the square plate (M1) = σ * a²
- Mass of the circular disc (M2) = σ * (πa²/4)
Positioning the Shapes
- The center of the square plate is at (a/2, a/2) in a Cartesian coordinate system.
- The center of the circular disc is at (0, a/4) since it is touching the edge of the square plate at its midpoint.
Finding the Center of Mass
The coordinates of the center of mass (COM) can be found using the formula:
COM = (M1 * x1 + M2 * x2) / (M1 + M2), (M1 * y1 + M2 * y2) / (M1 + M2)
Where:
- (x1, y1) = coordinates of the square plate's center
- (x2, y2) = coordinates of the circular disc's center
Substituting the values, we can determine the center of mass relative to the disc's center.
Final Calculation
After substituting the respective masses and coordinates into the formula, we can arrive at the distance from the center of the disc to the center of mass of the system.
This distance gives a clear understanding of the distribution of mass and how the two shapes interact in this combined system.
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A Square Plate of Edge a and a circular disc of same diameter are placed touching each other at the midpoint of the edge of the plate as shown in the figure if the mass per unit of the two plates are same then find the distance of centre of mass of the system from the centre of the disc?
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A Square Plate of Edge a and a circular disc of same diameter are placed touching each other at the midpoint of the edge of the plate as shown in the figure if the mass per unit of the two plates are same then find the distance of centre of mass of the system from the centre of the disc? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A Square Plate of Edge a and a circular disc of same diameter are placed touching each other at the midpoint of the edge of the plate as shown in the figure if the mass per unit of the two plates are same then find the distance of centre of mass of the system from the centre of the disc? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Square Plate of Edge a and a circular disc of same diameter are placed touching each other at the midpoint of the edge of the plate as shown in the figure if the mass per unit of the two plates are same then find the distance of centre of mass of the system from the centre of the disc?.
A Square Plate of Edge a and a circular disc of same diameter are placed touching each other at the midpoint of the edge of the plate as shown in the figure if the mass per unit of the two plates are same then find the distance of centre of mass of the system from the centre of the disc? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A Square Plate of Edge a and a circular disc of same diameter are placed touching each other at the midpoint of the edge of the plate as shown in the figure if the mass per unit of the two plates are same then find the distance of centre of mass of the system from the centre of the disc? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Square Plate of Edge a and a circular disc of same diameter are placed touching each other at the midpoint of the edge of the plate as shown in the figure if the mass per unit of the two plates are same then find the distance of centre of mass of the system from the centre of the disc?.
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