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Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Find the distance of their centre of mass from A.?
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Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the...
Step 1: Finding the coordinates of the particles
To find the distance of the center of mass from point A, we need to first determine the coordinates of the particles A, B, and C. Since the triangle ABC is equilateral, we can use the following coordinates:
A: (0, 0)
B: (1, 0)
C: (0.5, sqrt(3)/2)
Step 2: Finding the mass center
The center of mass is given by the equation:
x_cm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
y_cm = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)
where m1, m2, and m3 are the masses of the particles, and (x1, y1), (x2, y2), and (x3, y3) are their respective coordinates.
Step 3: Calculating the center of mass
Using the given masses and coordinates, we can calculate the center of mass:
x_cm = (1 * 0 + 2 * 1 + 3 * 0.5) / (1 + 2 + 3) = 1.5 / 6 = 0.25
y_cm = (1 * 0 + 2 * 0 + 3 * sqrt(3)/2) / (1 + 2 + 3) = (3 * sqrt(3)/2) / 6 = sqrt(3)/4
Therefore, the center of mass is located at (0.25, sqrt(3)/4).
Step 4: Finding the distance from A to the center of mass
To find the distance from point A to the center of mass, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of point A (0, 0) and the center of mass (0.25, sqrt(3)/4), we can calculate the distance:
d = sqrt((0.25 - 0)^2 + (sqrt(3)/4 - 0)^2)
d = sqrt(0.0625 + 3/16)
d = sqrt(0.4375 + 0.1875)
d = sqrt(0.625)
d ≈ 0.79 m
Therefore, the distance of the center of mass from point A is approximately 0.79 meters.
To find the distance of the center of mass from point A, we need to first determine the coordinates of the particles A, B, and C. Since the triangle ABC is equilateral, we can use the following coordinates:
A: (0, 0)
B: (1, 0)
C: (0.5, sqrt(3)/2)
Step 2: Finding the mass center
The center of mass is given by the equation:
x_cm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
y_cm = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)
where m1, m2, and m3 are the masses of the particles, and (x1, y1), (x2, y2), and (x3, y3) are their respective coordinates.
Step 3: Calculating the center of mass
Using the given masses and coordinates, we can calculate the center of mass:
x_cm = (1 * 0 + 2 * 1 + 3 * 0.5) / (1 + 2 + 3) = 1.5 / 6 = 0.25
y_cm = (1 * 0 + 2 * 0 + 3 * sqrt(3)/2) / (1 + 2 + 3) = (3 * sqrt(3)/2) / 6 = sqrt(3)/4
Therefore, the center of mass is located at (0.25, sqrt(3)/4).
Step 4: Finding the distance from A to the center of mass
To find the distance from point A to the center of mass, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of point A (0, 0) and the center of mass (0.25, sqrt(3)/4), we can calculate the distance:
d = sqrt((0.25 - 0)^2 + (sqrt(3)/4 - 0)^2)
d = sqrt(0.0625 + 3/16)
d = sqrt(0.4375 + 0.1875)
d = sqrt(0.625)
d ≈ 0.79 m
Therefore, the distance of the center of mass from point A is approximately 0.79 meters.
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Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Find the distance of their centre of mass from A.?
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Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Find the distance of their centre of mass from A.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Find the distance of their centre of mass from A.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Find the distance of their centre of mass from A.?.
Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Find the distance of their centre of mass from A.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Find the distance of their centre of mass from A.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ques 5: Three particles of mass 1 kg, 2 kg, and 3 kg are placed at the corners A, B and C respectively of an equilateral triangle ABC of edge 1 m. Find the distance of their centre of mass from A.?.
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