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A ring has greater moment of inertia than a circular disc of same mass and radius, about an axis passing through its centre of mass perpendicular to its plane, because
- a)all mass is at maximum distance from axis
- b)because the centre of the ring does not lie on it
- c)because the ring needs greater inertia to bend it
- d)because the moment produced in the ring is more
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A ring has greater moment of inertia than a circular disc of same mass...
A ring has a larger moment of inertia because its entire mass is concentrated at the rim at maximum distance from the axis.
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Most Upvoted Answer
A ring has greater moment of inertia than a circular disc of same mass...
Explanation:
Moment of inertia is defined as the resistance offered by a body to change its state of rotation about an axis. It is dependent on the mass distribution of the body and the distance of the particles from the axis of rotation.
The given question asks us to compare the moment of inertia of a ring and a disc of the same mass and radius, with the axis of rotation passing through their center of mass perpendicular to their plane.
The moment of inertia of a ring and a disc can be calculated using the formula:
Iring = MR²
Idisc = ½ MR²
where M is the mass of the body, and R is the radius of the body.
From the above formulas, we can see that the moment of inertia of the ring is greater than that of the disc.
Now, let's understand why this is so.
Mass distribution:
The mass of the ring is distributed uniformly along its circumference, whereas the mass of the disc is concentrated at its center.
In the case of the ring, all the particles are at the maximum distance from the axis of rotation, which means they contribute the most to the moment of inertia.
In the case of the disc, the particles near the center contribute very little to the moment of inertia, as they are very close to the axis of rotation.
Distance from axis:
As mentioned earlier, the particles in the ring are at a greater distance from the axis of rotation compared to the particles in the disc. This means that the particles in the ring contribute more to the moment of inertia compared to the particles in the disc.
Inertia to bending:
The option 'C' in the question suggests that the ring needs greater inertia to bend it, but this is not correct. Inertia is a property that opposes a change in the state of motion of a body, and bending does not involve any change in the state of motion of the body.
Moment produced:
The option 'D' in the question suggests that the moment produced in the ring is more, but this is not correct either. The moment produced depends on the force applied and the distance from the axis of rotation. It is not a property of the body itself.
Therefore, the correct answer to the given question is option 'A' - all mass is at maximum distance from the axis.
Moment of inertia is defined as the resistance offered by a body to change its state of rotation about an axis. It is dependent on the mass distribution of the body and the distance of the particles from the axis of rotation.
The given question asks us to compare the moment of inertia of a ring and a disc of the same mass and radius, with the axis of rotation passing through their center of mass perpendicular to their plane.
The moment of inertia of a ring and a disc can be calculated using the formula:
Iring = MR²
Idisc = ½ MR²
where M is the mass of the body, and R is the radius of the body.
From the above formulas, we can see that the moment of inertia of the ring is greater than that of the disc.
Now, let's understand why this is so.
Mass distribution:
The mass of the ring is distributed uniformly along its circumference, whereas the mass of the disc is concentrated at its center.
In the case of the ring, all the particles are at the maximum distance from the axis of rotation, which means they contribute the most to the moment of inertia.
In the case of the disc, the particles near the center contribute very little to the moment of inertia, as they are very close to the axis of rotation.
Distance from axis:
As mentioned earlier, the particles in the ring are at a greater distance from the axis of rotation compared to the particles in the disc. This means that the particles in the ring contribute more to the moment of inertia compared to the particles in the disc.
Inertia to bending:
The option 'C' in the question suggests that the ring needs greater inertia to bend it, but this is not correct. Inertia is a property that opposes a change in the state of motion of a body, and bending does not involve any change in the state of motion of the body.
Moment produced:
The option 'D' in the question suggests that the moment produced in the ring is more, but this is not correct either. The moment produced depends on the force applied and the distance from the axis of rotation. It is not a property of the body itself.
Therefore, the correct answer to the given question is option 'A' - all mass is at maximum distance from the axis.
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A ring has greater moment of inertia than a circular disc of same mass...
Answer A is correct
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A ring has greater moment of inertia than a circular disc of same mass and radius, about an axis passing through its centre of mass perpendicular to its plane, becausea)all mass is at maximum distance from axisb)because the centre of the ring does not lie on itc)because the ring needs greater inertia to bend itd)because the moment produced in the ring is moreCorrect answer is option 'A'. Can you explain this answer?
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A ring has greater moment of inertia than a circular disc of same mass and radius, about an axis passing through its centre of mass perpendicular to its plane, becausea)all mass is at maximum distance from axisb)because the centre of the ring does not lie on itc)because the ring needs greater inertia to bend itd)because the moment produced in the ring is moreCorrect answer is option 'A'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A ring has greater moment of inertia than a circular disc of same mass and radius, about an axis passing through its centre of mass perpendicular to its plane, becausea)all mass is at maximum distance from axisb)because the centre of the ring does not lie on itc)because the ring needs greater inertia to bend itd)because the moment produced in the ring is moreCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ring has greater moment of inertia than a circular disc of same mass and radius, about an axis passing through its centre of mass perpendicular to its plane, becausea)all mass is at maximum distance from axisb)because the centre of the ring does not lie on itc)because the ring needs greater inertia to bend itd)because the moment produced in the ring is moreCorrect answer is option 'A'. Can you explain this answer?.
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