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A uniform square plate ABCD has mass of 10 kg. If two points of masses 3 kg each are placed at the corners C and D as shown in fig. then the centre of mass shifts to the point which lie on?
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A uniform square plate ABCD has mass of 10 kg. If two points of masses...
Understanding the System
The system consists of a uniform square plate ABCD with mass 10 kg and two point masses of 3 kg each placed at corners C and D. To find the new center of mass, we can use the concept of the center of mass (COM) for a system of particles.
Coordinates of the Plate and Masses
- Assume the square plate has its corners at the following coordinates:
- A(0, 0)
- B(1, 0)
- C(1, 1)
- D(0, 1)
- The mass of the plate is uniformly distributed, so the center of mass of the plate (without added masses) is at:
- COM of Plate = (0.5, 0.5)
- The point masses are located at:
- Mass at C = 3 kg
- Mass at D = 3 kg
Calculating the New Center of Mass
- The total mass of the system is:
- Total Mass = 10 kg (plate) + 3 kg (C) + 3 kg (D) = 16 kg
- The x-coordinate of the new COM is calculated as:
- X_COM = (10 kg * 0.5 + 3 kg * 1 + 3 kg * 0) / 16 kg
- X_COM = (5 + 3) / 16 = 0.5
- The y-coordinate of the new COM is:
- Y_COM = (10 kg * 0.5 + 3 kg * 1 + 3 kg * 1) / 16 kg
- Y_COM = (5 + 3 + 3) / 16 = 0.6875
Conclusion
The new center of mass of the system lies at the coordinates (0.5, 0.6875). This indicates a shift upward due to the additional masses placed at corners C and D, which increases the influence on the overall center of mass in the vertical direction.
The system consists of a uniform square plate ABCD with mass 10 kg and two point masses of 3 kg each placed at corners C and D. To find the new center of mass, we can use the concept of the center of mass (COM) for a system of particles.
Coordinates of the Plate and Masses
- Assume the square plate has its corners at the following coordinates:
- A(0, 0)
- B(1, 0)
- C(1, 1)
- D(0, 1)
- The mass of the plate is uniformly distributed, so the center of mass of the plate (without added masses) is at:
- COM of Plate = (0.5, 0.5)
- The point masses are located at:
- Mass at C = 3 kg
- Mass at D = 3 kg
Calculating the New Center of Mass
- The total mass of the system is:
- Total Mass = 10 kg (plate) + 3 kg (C) + 3 kg (D) = 16 kg
- The x-coordinate of the new COM is calculated as:
- X_COM = (10 kg * 0.5 + 3 kg * 1 + 3 kg * 0) / 16 kg
- X_COM = (5 + 3) / 16 = 0.5
- The y-coordinate of the new COM is:
- Y_COM = (10 kg * 0.5 + 3 kg * 1 + 3 kg * 1) / 16 kg
- Y_COM = (5 + 3 + 3) / 16 = 0.6875
Conclusion
The new center of mass of the system lies at the coordinates (0.5, 0.6875). This indicates a shift upward due to the additional masses placed at corners C and D, which increases the influence on the overall center of mass in the vertical direction.
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A uniform square plate ABCD has mass of 10 kg. If two points of masses 3 kg each are placed at the corners C and D as shown in fig. then the centre of mass shifts to the point which lie on?
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A uniform square plate ABCD has mass of 10 kg. If two points of masses 3 kg each are placed at the corners C and D as shown in fig. then the centre of mass shifts to the point which lie on? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A uniform square plate ABCD has mass of 10 kg. If two points of masses 3 kg each are placed at the corners C and D as shown in fig. then the centre of mass shifts to the point which lie on? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform square plate ABCD has mass of 10 kg. If two points of masses 3 kg each are placed at the corners C and D as shown in fig. then the centre of mass shifts to the point which lie on?.
A uniform square plate ABCD has mass of 10 kg. If two points of masses 3 kg each are placed at the corners C and D as shown in fig. then the centre of mass shifts to the point which lie on? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A uniform square plate ABCD has mass of 10 kg. If two points of masses 3 kg each are placed at the corners C and D as shown in fig. then the centre of mass shifts to the point which lie on? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform square plate ABCD has mass of 10 kg. If two points of masses 3 kg each are placed at the corners C and D as shown in fig. then the centre of mass shifts to the point which lie on?.
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