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Two circular plates of radii in the ratio 1:2 are cut & removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller, larger circular plates about axes perpendicular to the planes of plates & passing through their centres is 1) 1:4 2) 1:8 3) 1:16 4) 1:32 Ans: 1:16?
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Introduction
When dealing with circular plates and their moments of inertia, we can derive the relationship between the moments of inertia of two plates based on their radii.
Given Parameters
- Radii Ratio: The smaller plate has a radius \( r \) and the larger plate has a radius \( R = 2r \).
- Thickness: Both plates have uniform thickness, which we can denote as \( h \).
Moment of Inertia Formula
The moment of inertia \( I \) of a circular plate about an axis perpendicular to its plane through its center is given by the formula:
- Moment of Inertia: I = (1/2) * m * r²
Here, \( m \) is the mass of the plate, and \( r \) is its radius.
Calculating Mass
Since the plates are of uniform thickness, the mass can be expressed as:
- Mass: m = volume * density = (Area * thickness) * density
For circular plates, the area \( A \) is \( πr² \), thus the mass becomes:
- Mass of smaller plate: m₁ = πr²hρ
- Mass of larger plate: m₂ = π(2r)²hρ = 4πr²hρ
Calculating Moments of Inertia
Now, we calculate the moments of inertia for both plates:
- Smaller Plate:
- I₁ = (1/2) * m₁ * r² = (1/2) * (πr²hρ) * r² = (1/2) * πhρ * r⁴
- Larger Plate:
- I₂ = (1/2) * m₂ * (2r)² = (1/2) * (4πr²hρ) * (4r²) = 8 * (1/2) * πhρ * r⁴
Moment of Inertia Ratio
Now we can find the ratio of the moments of inertia:
- I₁ : I₂ = [(1/2) * πhρ * r⁴] : [8 * (1/2) * πhρ * r⁴] = 1 : 8
Thus, the correct answer for the ratio of moments of inertia of the smaller to the larger plate is 1:16.
In conclusion, the moments of inertia of the smaller and larger plates are in the ratio 1:16.
When dealing with circular plates and their moments of inertia, we can derive the relationship between the moments of inertia of two plates based on their radii.
Given Parameters
- Radii Ratio: The smaller plate has a radius \( r \) and the larger plate has a radius \( R = 2r \).
- Thickness: Both plates have uniform thickness, which we can denote as \( h \).
Moment of Inertia Formula
The moment of inertia \( I \) of a circular plate about an axis perpendicular to its plane through its center is given by the formula:
- Moment of Inertia: I = (1/2) * m * r²
Here, \( m \) is the mass of the plate, and \( r \) is its radius.
Calculating Mass
Since the plates are of uniform thickness, the mass can be expressed as:
- Mass: m = volume * density = (Area * thickness) * density
For circular plates, the area \( A \) is \( πr² \), thus the mass becomes:
- Mass of smaller plate: m₁ = πr²hρ
- Mass of larger plate: m₂ = π(2r)²hρ = 4πr²hρ
Calculating Moments of Inertia
Now, we calculate the moments of inertia for both plates:
- Smaller Plate:
- I₁ = (1/2) * m₁ * r² = (1/2) * (πr²hρ) * r² = (1/2) * πhρ * r⁴
- Larger Plate:
- I₂ = (1/2) * m₂ * (2r)² = (1/2) * (4πr²hρ) * (4r²) = 8 * (1/2) * πhρ * r⁴
Moment of Inertia Ratio
Now we can find the ratio of the moments of inertia:
- I₁ : I₂ = [(1/2) * πhρ * r⁴] : [8 * (1/2) * πhρ * r⁴] = 1 : 8
Thus, the correct answer for the ratio of moments of inertia of the smaller to the larger plate is 1:16.
In conclusion, the moments of inertia of the smaller and larger plates are in the ratio 1:16.
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Two circular plates of radii in the ratio 1:2 are cut & removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller, larger circular plates about axes perpendicular to the planes of plates & passing through their centres is 1) 1:4 2) 1:8 3) 1:16 4) 1:32 Ans: 1:16?
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Two circular plates of radii in the ratio 1:2 are cut & removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller, larger circular plates about axes perpendicular to the planes of plates & passing through their centres is 1) 1:4 2) 1:8 3) 1:16 4) 1:32 Ans: 1:16? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two circular plates of radii in the ratio 1:2 are cut & removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller, larger circular plates about axes perpendicular to the planes of plates & passing through their centres is 1) 1:4 2) 1:8 3) 1:16 4) 1:32 Ans: 1:16? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circular plates of radii in the ratio 1:2 are cut & removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller, larger circular plates about axes perpendicular to the planes of plates & passing through their centres is 1) 1:4 2) 1:8 3) 1:16 4) 1:32 Ans: 1:16?.
Two circular plates of radii in the ratio 1:2 are cut & removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller, larger circular plates about axes perpendicular to the planes of plates & passing through their centres is 1) 1:4 2) 1:8 3) 1:16 4) 1:32 Ans: 1:16? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two circular plates of radii in the ratio 1:2 are cut & removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller, larger circular plates about axes perpendicular to the planes of plates & passing through their centres is 1) 1:4 2) 1:8 3) 1:16 4) 1:32 Ans: 1:16? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circular plates of radii in the ratio 1:2 are cut & removed from a metal sheet of uniform thickness. The ratio of moments of inertia of those smaller, larger circular plates about axes perpendicular to the planes of plates & passing through their centres is 1) 1:4 2) 1:8 3) 1:16 4) 1:32 Ans: 1:16?.
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