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Four particles A,B,C,D having masses m,2m,3m,4m respectively are placed in order at the corners of a square of side a . Locate the centre of mass 1. (a,7/10) 2 (a/2,7a/10) 3.(a/4,14a) 4. (a,5a)?
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Four particles A,B,C,D having masses m,2m,3m,4m respectively are place...
Centre of Mass of a System of Particles
To find the centre of mass of a system of particles, we need to consider the position and mass of each particle and calculate the weighted average of their positions.
Given:
Particles A, B, C, and D with masses m, 2m, 3m, and 4m respectively.
They are placed in order at the corners of a square of side a.
Using the concept of centre of mass, we can calculate the position of the centre of mass of this system.
1. Find the position of the centre of mass in the x-direction:
To calculate the x-coordinate of the centre of mass, we use the formula:
x_cm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
- Particle A is located at the origin (0, 0), so its position is (0, 0) and its mass is m.
- Particle B is located at the point (a, 0), so its position is (a, 0) and its mass is 2m.
- Particle C is located at the point (a, a), so its position is (a, a) and its mass is 3m.
- Particle D is located at the point (0, a), so its position is (0, a) and its mass is 4m.
Now, substituting these values into the formula:
x_cm = (m * 0 + 2m * a + 3m * a + 4m * 0) / (m + 2m + 3m + 4m)
x_cm = (2ma + 3ma) / (10m)
x_cm = 5a / 10
x_cm = a / 2
2. Find the position of the centre of mass in the y-direction:
To calculate the y-coordinate of the centre of mass, we use the formula:
y_cm = (m1y1 + m2y2 + m3y3 + m4y4) / (m1 + m2 + m3 + m4)
- Particle A is located at the origin (0, 0), so its position is (0, 0) and its mass is m.
- Particle B is located at the point (a, 0), so its position is (a, 0) and its mass is 2m.
- Particle C is located at the point (a, a), so its position is (a, a) and its mass is 3m.
- Particle D is located at the point (0, a), so its position is (0, a) and its mass is 4m.
Now, substituting these values into the formula:
y_cm = (m * 0 + 2m * 0 + 3m * a + 4m * a) / (m + 2m + 3m + 4m)
y_cm = (7ma) / (10m)
y_cm = 7a / 10
Therefore, the position of the centre of mass is (a/2, 7a/10).
The correct answer is option 2: (a/2, 7a/10).
To find the centre of mass of a system of particles, we need to consider the position and mass of each particle and calculate the weighted average of their positions.
Given:
Particles A, B, C, and D with masses m, 2m, 3m, and 4m respectively.
They are placed in order at the corners of a square of side a.
Using the concept of centre of mass, we can calculate the position of the centre of mass of this system.
1. Find the position of the centre of mass in the x-direction:
To calculate the x-coordinate of the centre of mass, we use the formula:
x_cm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
- Particle A is located at the origin (0, 0), so its position is (0, 0) and its mass is m.
- Particle B is located at the point (a, 0), so its position is (a, 0) and its mass is 2m.
- Particle C is located at the point (a, a), so its position is (a, a) and its mass is 3m.
- Particle D is located at the point (0, a), so its position is (0, a) and its mass is 4m.
Now, substituting these values into the formula:
x_cm = (m * 0 + 2m * a + 3m * a + 4m * 0) / (m + 2m + 3m + 4m)
x_cm = (2ma + 3ma) / (10m)
x_cm = 5a / 10
x_cm = a / 2
2. Find the position of the centre of mass in the y-direction:
To calculate the y-coordinate of the centre of mass, we use the formula:
y_cm = (m1y1 + m2y2 + m3y3 + m4y4) / (m1 + m2 + m3 + m4)
- Particle A is located at the origin (0, 0), so its position is (0, 0) and its mass is m.
- Particle B is located at the point (a, 0), so its position is (a, 0) and its mass is 2m.
- Particle C is located at the point (a, a), so its position is (a, a) and its mass is 3m.
- Particle D is located at the point (0, a), so its position is (0, a) and its mass is 4m.
Now, substituting these values into the formula:
y_cm = (m * 0 + 2m * 0 + 3m * a + 4m * a) / (m + 2m + 3m + 4m)
y_cm = (7ma) / (10m)
y_cm = 7a / 10
Therefore, the position of the centre of mass is (a/2, 7a/10).
The correct answer is option 2: (a/2, 7a/10).
Community Answer
Four particles A,B,C,D having masses m,2m,3m,4m respectively are place...
Ans:2
use formula of c.o.m
€mi.xi/€xi for x axis and yaxis respectively
use formula of c.o.m
€mi.xi/€xi for x axis and yaxis respectively
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Four particles A,B,C,D having masses m,2m,3m,4m respectively are placed in order at the corners of a square of side a . Locate the centre of mass 1. (a,7/10) 2 (a/2,7a/10) 3.(a/4,14a) 4. (a,5a)?
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Four particles A,B,C,D having masses m,2m,3m,4m respectively are placed in order at the corners of a square of side a . Locate the centre of mass 1. (a,7/10) 2 (a/2,7a/10) 3.(a/4,14a) 4. (a,5a)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Four particles A,B,C,D having masses m,2m,3m,4m respectively are placed in order at the corners of a square of side a . Locate the centre of mass 1. (a,7/10) 2 (a/2,7a/10) 3.(a/4,14a) 4. (a,5a)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four particles A,B,C,D having masses m,2m,3m,4m respectively are placed in order at the corners of a square of side a . Locate the centre of mass 1. (a,7/10) 2 (a/2,7a/10) 3.(a/4,14a) 4. (a,5a)?.
Four particles A,B,C,D having masses m,2m,3m,4m respectively are placed in order at the corners of a square of side a . Locate the centre of mass 1. (a,7/10) 2 (a/2,7a/10) 3.(a/4,14a) 4. (a,5a)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Four particles A,B,C,D having masses m,2m,3m,4m respectively are placed in order at the corners of a square of side a . Locate the centre of mass 1. (a,7/10) 2 (a/2,7a/10) 3.(a/4,14a) 4. (a,5a)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four particles A,B,C,D having masses m,2m,3m,4m respectively are placed in order at the corners of a square of side a . Locate the centre of mass 1. (a,7/10) 2 (a/2,7a/10) 3.(a/4,14a) 4. (a,5a)?.
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