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Three particles ofmasses 1 kg, 2 kg, 2kg are placed at the corners of an equilateral triangle ABC where coordinates of A and B are (0, 0) and (2, 0) respectively. then what is the coordinates of C. O. M of the system.?
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Calculating the Center of Mass of the System
To find the coordinates of the center of mass of the system consisting of three particles placed at the corners of an equilateral triangle, we can use the formula:
$$x_{\text{COM}} = \frac{m_1x_1 + m_2x_2 + m_3x_3}{m_1 + m_2 + m_3}$$
$$y_{\text{COM}} = \frac{m_1y_1 + m_2y_2 + m_3y_3}{m_1 + m_2 + m_3}$$
where \(m_i\) are the masses of the particles and \(x_i, y_i\) are their coordinates.
Coordinates of Particles A, B, and C
- Particle A: (0, 0), mass = 1 kg
- Particle B: (2, 0), mass = 2 kg
- Particle C: Let the coordinates of C be (x, y) and mass = 2 kg
Using the Formula
- For x-coordinate:
- \(x_{\text{COM}} = \frac{1 \times 0 + 2 \times 2 + 2 \times x}{1 + 2 + 2}\)
- \(x_{\text{COM}} = \frac{4 + 2x}{5}\)
- For y-coordinate:
- \(y_{\text{COM}} = \frac{1 \times 0 + 2 \times 0 + 2 \times y}{1 + 2 + 2}\)
- \(y_{\text{COM}} = \frac{2y}{5}\)
Since the triangle is equilateral, the centroid coincides with the center of mass. Therefore, the coordinates of the center of mass will be the coordinates of point C.
Solving for C
- Equating the x and y coordinates:
- \(x_{\text{COM}} = x = \frac{4 + 2x}{5}\)
- Solving for x, we get: \(x = \frac{4}{3}\)
- \(y_{\text{COM}} = y = \frac{2y}{5}\)
- Solving for y, we get: \(y = 0\)
Hence, the coordinates of point C (center of mass) are \(\left(\frac{4}{3}, 0\right)\).
To find the coordinates of the center of mass of the system consisting of three particles placed at the corners of an equilateral triangle, we can use the formula:
where \(m_i\) are the masses of the particles and \(x_i, y_i\) are their coordinates.
Coordinates of Particles A, B, and C
- Particle A: (0, 0), mass = 1 kg
- Particle B: (2, 0), mass = 2 kg
- Particle C: Let the coordinates of C be (x, y) and mass = 2 kg
Using the Formula
- For x-coordinate:
- \(x_{\text{COM}} = \frac{1 \times 0 + 2 \times 2 + 2 \times x}{1 + 2 + 2}\)
- \(x_{\text{COM}} = \frac{4 + 2x}{5}\)
- For y-coordinate:
- \(y_{\text{COM}} = \frac{1 \times 0 + 2 \times 0 + 2 \times y}{1 + 2 + 2}\)
- \(y_{\text{COM}} = \frac{2y}{5}\)
Since the triangle is equilateral, the centroid coincides with the center of mass. Therefore, the coordinates of the center of mass will be the coordinates of point C.
Solving for C
- Equating the x and y coordinates:
- \(x_{\text{COM}} = x = \frac{4 + 2x}{5}\)
- Solving for x, we get: \(x = \frac{4}{3}\)
- \(y_{\text{COM}} = y = \frac{2y}{5}\)
- Solving for y, we get: \(y = 0\)
Hence, the coordinates of point C (center of mass) are \(\left(\frac{4}{3}, 0\right)\).
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Three particles ofmasses 1 kg, 2 kg, 2kg are placed at the corners of an equilateral triangle ABC where coordinates of A and B are (0, 0) and (2, 0) respectively. then what is the coordinates of C. O. M of the system.?
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Three particles ofmasses 1 kg, 2 kg, 2kg are placed at the corners of an equilateral triangle ABC where coordinates of A and B are (0, 0) and (2, 0) respectively. then what is the coordinates of C. O. M of the system.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Three particles ofmasses 1 kg, 2 kg, 2kg are placed at the corners of an equilateral triangle ABC where coordinates of A and B are (0, 0) and (2, 0) respectively. then what is the coordinates of C. O. M of the system.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three particles ofmasses 1 kg, 2 kg, 2kg are placed at the corners of an equilateral triangle ABC where coordinates of A and B are (0, 0) and (2, 0) respectively. then what is the coordinates of C. O. M of the system.?.
Three particles ofmasses 1 kg, 2 kg, 2kg are placed at the corners of an equilateral triangle ABC where coordinates of A and B are (0, 0) and (2, 0) respectively. then what is the coordinates of C. O. M of the system.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Three particles ofmasses 1 kg, 2 kg, 2kg are placed at the corners of an equilateral triangle ABC where coordinates of A and B are (0, 0) and (2, 0) respectively. then what is the coordinates of C. O. M of the system.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three particles ofmasses 1 kg, 2 kg, 2kg are placed at the corners of an equilateral triangle ABC where coordinates of A and B are (0, 0) and (2, 0) respectively. then what is the coordinates of C. O. M of the system.?.
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