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Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio
- a)1 : 3
- b)3 : 1
- c)1 : 9
- d)9 : 1
Correct answer is option 'B'. Can you explain this answer?
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Mass and Density Relationship
The given problem states that two discs have the same mass but different densities. Let's assume the mass of each disc is 'm'. Since the discs have the same mass, their masses can be represented as 'm' and 'm' respectively.
Density Relationship
The problem further states that the densities of the materials are in the ratio 1:3. Let's assume the densities of the two materials are 'd1' and 'd2' respectively. According to the given information, we have the following relationship between the densities:
d1 : d2 = 1 : 3
Formula for Density
Density is defined as the ratio of mass to volume. Mathematically, it can be represented as:
Density = Mass / Volume
Formula for Volume
The volume of a disc can be calculated using its radius and thickness. Mathematically, it can be represented as:
Volume = π * r^2 * h
Using the above formulas, we can relate the densities of the two discs as follows:
For Disc 1:
Density1 = m / (π * r1^2 * h)
For Disc 2:
Density2 = m / (π * r2^2 * h)
Since the mass of both discs is the same, we can equate the two equations:
m / (π * r1^2 * h) = m / (π * r2^2 * h)
Simplifying the equation, we get:
r1^2 / r2^2 = 1
This implies that the ratio of the squares of the radii of the two discs is 1.
Relationship between Moments of Inertia
The moment of inertia of a disc about an axis passing through its center and perpendicular to its plane can be calculated using the formula:
I = (m * r^2) / 2
Using this formula, the moments of inertia of the two discs can be represented as follows:
For Disc 1:
I1 = (m * r1^2) / 2
For Disc 2:
I2 = (m * r2^2) / 2
Since the masses of both discs are the same, we can equate the two equations:
(m * r1^2) / 2 = (m * r2^2) / 2
Simplifying the equation, we get:
r1^2 / r2^2 = 1
Again, we find that the ratio of the squares of the radii of the two discs is 1.
Ratio of Moments of Inertia
Since the ratio of the squares of the radii of the two discs is 1, the ratio of their moments of inertia will also be 1.
Therefore, the correct answer is option B: 3 : 1.
The given problem states that two discs have the same mass but different densities. Let's assume the mass of each disc is 'm'. Since the discs have the same mass, their masses can be represented as 'm' and 'm' respectively.
Density Relationship
The problem further states that the densities of the materials are in the ratio 1:3. Let's assume the densities of the two materials are 'd1' and 'd2' respectively. According to the given information, we have the following relationship between the densities:
d1 : d2 = 1 : 3
Formula for Density
Density is defined as the ratio of mass to volume. Mathematically, it can be represented as:
Density = Mass / Volume
Formula for Volume
The volume of a disc can be calculated using its radius and thickness. Mathematically, it can be represented as:
Volume = π * r^2 * h
Using the above formulas, we can relate the densities of the two discs as follows:
For Disc 1:
Density1 = m / (π * r1^2 * h)
For Disc 2:
Density2 = m / (π * r2^2 * h)
Since the mass of both discs is the same, we can equate the two equations:
m / (π * r1^2 * h) = m / (π * r2^2 * h)
Simplifying the equation, we get:
r1^2 / r2^2 = 1
This implies that the ratio of the squares of the radii of the two discs is 1.
Relationship between Moments of Inertia
The moment of inertia of a disc about an axis passing through its center and perpendicular to its plane can be calculated using the formula:
I = (m * r^2) / 2
Using this formula, the moments of inertia of the two discs can be represented as follows:
For Disc 1:
I1 = (m * r1^2) / 2
For Disc 2:
I2 = (m * r2^2) / 2
Since the masses of both discs are the same, we can equate the two equations:
(m * r1^2) / 2 = (m * r2^2) / 2
Simplifying the equation, we get:
r1^2 / r2^2 = 1
Again, we find that the ratio of the squares of the radii of the two discs is 1.
Ratio of Moments of Inertia
Since the ratio of the squares of the radii of the two discs is 1, the ratio of their moments of inertia will also be 1.
Therefore, the correct answer is option B: 3 : 1.
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Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratioa)1 : 3b)3 : 1c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer?
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Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratioa)1 : 3b)3 : 1c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratioa)1 : 3b)3 : 1c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratioa)1 : 3b)3 : 1c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer?.
Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratioa)1 : 3b)3 : 1c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratioa)1 : 3b)3 : 1c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1:3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratioa)1 : 3b)3 : 1c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer?.
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