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A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α / R form the centre of the bigger disc. The value of α is
- a)1/4
- b)1/3
- c)1/2
- d)1/6
Correct answer is option 'B'. Can you explain this answer?
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A circular disc of radius R is removed from a bigger circular disc of ...
Let the mass per unit area beσ.
Then the mass of the complete disc
Then the mass of the complete disc
The mass of the removed disc 
Let us consider the above situation to be a complete disc of radius 2R on which a disc of radius R of negative mass is superimposed. Let O be the origin. Then the above figure can be redrawn keeping in mind the concept of centre of mass as : 
Let us consider the above situation to be a complete disc of radius 2R on which a disc of radius R of negative mass is superimposed. Let O be the origin. Then the above figure can be redrawn keeping in mind the concept of centre of mass as : Most Upvoted Answer
A circular disc of radius R is removed from a bigger circular disc of ...
To find the center of mass of the new disc, we need to consider the center of mass of the original disc and the removed disc separately.
The center of mass of a uniform circular disc is at its geometric center. Since the original disc has a radius of 2R, its center of mass is at a distance of R from its center.
The removed disc has a radius of R, so its center of mass is at a distance of R/2 from its center.
When the two discs are placed together such that their circumferences coincide, the center of mass of the new disc can be found by considering the weighted average of the positions of the centers of mass of the two discs.
Let's assume that the center of mass of the original disc is at the origin (0,0) on a coordinate plane. Then, the center of mass of the removed disc is at (0, -R/2).
To find the center of mass of the new disc, we can use the formula for the weighted average:
x̅ = (m₁x₁ + m₂x₂) / (m₁ + m₂)
where x̅ is the x-coordinate of the center of mass, m₁ and m₂ are the masses of the two discs, and x₁ and x₂ are the x-coordinates of their centers of mass.
In this case, the masses of the two discs are equal because they have the same circumference. So, we can simplify the formula to:
x̅ = (x₁ + x₂) / 2
Plugging in the values, we have:
x̅ = (0 + 0) / 2 = 0
Therefore, the x-coordinate of the center of mass of the new disc is 0.
Similarly, we can find the y-coordinate of the center of mass using the same formula:
y̅ = (m₁y₁ + m₂y₂) / (m₁ + m₂)
In this case, the y-coordinates of the centers of mass are -R and -R/2 for the original and removed discs, respectively.
Plugging in the values, we have:
y̅ = (R(-R) + R/2(-R/2)) / (R + R/2)
= (-R² - R²/4) / (3R/2)
= -4R/3
Therefore, the y-coordinate of the center of mass of the new disc is -4R/3.
In summary, the center of mass of the new disc is at the coordinates (0, -4R/3).
The center of mass of a uniform circular disc is at its geometric center. Since the original disc has a radius of 2R, its center of mass is at a distance of R from its center.
The removed disc has a radius of R, so its center of mass is at a distance of R/2 from its center.
When the two discs are placed together such that their circumferences coincide, the center of mass of the new disc can be found by considering the weighted average of the positions of the centers of mass of the two discs.
Let's assume that the center of mass of the original disc is at the origin (0,0) on a coordinate plane. Then, the center of mass of the removed disc is at (0, -R/2).
To find the center of mass of the new disc, we can use the formula for the weighted average:
x̅ = (m₁x₁ + m₂x₂) / (m₁ + m₂)
where x̅ is the x-coordinate of the center of mass, m₁ and m₂ are the masses of the two discs, and x₁ and x₂ are the x-coordinates of their centers of mass.
In this case, the masses of the two discs are equal because they have the same circumference. So, we can simplify the formula to:
x̅ = (x₁ + x₂) / 2
Plugging in the values, we have:
x̅ = (0 + 0) / 2 = 0
Therefore, the x-coordinate of the center of mass of the new disc is 0.
Similarly, we can find the y-coordinate of the center of mass using the same formula:
y̅ = (m₁y₁ + m₂y₂) / (m₁ + m₂)
In this case, the y-coordinates of the centers of mass are -R and -R/2 for the original and removed discs, respectively.
Plugging in the values, we have:
y̅ = (R(-R) + R/2(-R/2)) / (R + R/2)
= (-R² - R²/4) / (3R/2)
= -4R/3
Therefore, the y-coordinate of the center of mass of the new disc is -4R/3.
In summary, the center of mass of the new disc is at the coordinates (0, -4R/3).
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A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α / R form the centre of the bigger disc. The value of α isa)1/4b)1/3c)1/2d)1/6Correct answer is option 'B'. Can you explain this answer?
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A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α / R form the centre of the bigger disc. The value of α isa)1/4b)1/3c)1/2d)1/6Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α / R form the centre of the bigger disc. The value of α isa)1/4b)1/3c)1/2d)1/6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α / R form the centre of the bigger disc. The value of α isa)1/4b)1/3c)1/2d)1/6Correct answer is option 'B'. Can you explain this answer?.
A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α / R form the centre of the bigger disc. The value of α isa)1/4b)1/3c)1/2d)1/6Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α / R form the centre of the bigger disc. The value of α isa)1/4b)1/3c)1/2d)1/6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α / R form the centre of the bigger disc. The value of α isa)1/4b)1/3c)1/2d)1/6Correct answer is option 'B'. Can you explain this answer?.
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