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There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.?
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There are two masses m, and m_{2} are placed at a distance /apart, let...
Problem Statement:
There are two masses m and m2 placed at a distance /apart. Let the centre of mass of this system be at a point named m1 which is displaced by l1 towards C and m2 is displaced by l2 away from C. We need to find the distance from C where the new centre of mass will be located.
Solution:
Step 1: Identifying the Initial Centre of Mass
The initial centre of mass of the system can be found using the formula:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
Where,
- x_cm is the position of the centre of mass
- m1 and m2 are the masses of the two objects
- x1 and x2 are the distances of the two objects from the reference point (in this case, C)
Step 2: Displacement of the Centre of Mass
Now, we need to find the new position of the centre of mass when m1 is displaced by l1 towards C and m2 is displaced by l2 away from C.
Since the total mass of the system remains the same, the new centre of mass can be found using the formula:
x_new_cm = (m1 * (x1 + l1) + m2 * (x2 - l2)) / (m1 + m2)
Step 3: Simplifying the Equation
Expanding the equation, we get:
x_new_cm = (m1 * x1 + m1 * l1 + m2 * x2 - m2 * l2) / (m1 + m2)
Simplifying further, we get:
x_new_cm = (m1 * x1 + m2 * x2 + m1 * l1 - m2 * l2) / (m1 + m2)
Step 4: Finding the Distance from C
To find the distance from C where the new centre of mass is located, we subtract the initial position of the centre of mass from the new position:
Distance from C = x_new_cm - x_cm
Substituting the values, we get:
Distance from C = [(m1 * x1 + m2 * x2 + m1 * l1 - m2 * l2) / (m1 + m2)] - [(m1 * x1 + m2 * x2) / (m1 + m2)]
Simplifying further, we get:
Distance from C = (m1 * l1 - m2 * l2) / (m1 + m2)
Therefore, the distance from C where the new centre of mass will be located is (m1 * l1 - m2 * l2) / (m1 + m2).
There are two masses m and m2 placed at a distance /apart. Let the centre of mass of this system be at a point named m1 which is displaced by l1 towards C and m2 is displaced by l2 away from C. We need to find the distance from C where the new centre of mass will be located.
Solution:
Step 1: Identifying the Initial Centre of Mass
The initial centre of mass of the system can be found using the formula:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
Where,
- x_cm is the position of the centre of mass
- m1 and m2 are the masses of the two objects
- x1 and x2 are the distances of the two objects from the reference point (in this case, C)
Step 2: Displacement of the Centre of Mass
Now, we need to find the new position of the centre of mass when m1 is displaced by l1 towards C and m2 is displaced by l2 away from C.
Since the total mass of the system remains the same, the new centre of mass can be found using the formula:
x_new_cm = (m1 * (x1 + l1) + m2 * (x2 - l2)) / (m1 + m2)
Step 3: Simplifying the Equation
Expanding the equation, we get:
x_new_cm = (m1 * x1 + m1 * l1 + m2 * x2 - m2 * l2) / (m1 + m2)
Simplifying further, we get:
x_new_cm = (m1 * x1 + m2 * x2 + m1 * l1 - m2 * l2) / (m1 + m2)
Step 4: Finding the Distance from C
To find the distance from C where the new centre of mass is located, we subtract the initial position of the centre of mass from the new position:
Distance from C = x_new_cm - x_cm
Substituting the values, we get:
Distance from C = [(m1 * x1 + m2 * x2 + m1 * l1 - m2 * l2) / (m1 + m2)] - [(m1 * x1 + m2 * x2) / (m1 + m2)]
Simplifying further, we get:
Distance from C = (m1 * l1 - m2 * l2) / (m1 + m2)
Therefore, the distance from C where the new centre of mass will be located is (m1 * l1 - m2 * l2) / (m1 + m2).
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There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.?
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There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.?.
There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.?.
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There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.?, a detailed solution for There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.? has been provided alongside types of There are two masses m, and m_{2} are placed at a distance /apart, let the centre of mass of this system is at a point namedm_{1} is displaced by l_{1} towards C and m_{2} is displaced by I_{2}away from C. Find the distance, from C where new centre ofmass will be located.? theory, EduRev gives you an
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