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Two cylinders have the same mass and radius. One is hollow and the other is solid. Which one will have the greater moment of inertia about the central axis?
- a)Hollow cylinder
- b)Solid cylinder
- c)Same for both
- d)Depends on length of cylinder
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two cylinders have the same mass and radius. One is hollow and the oth...
Explanation:
1. Introduction:
In this question, we are given two cylinders with the same mass and radius. One cylinder is hollow, while the other is solid. We need to determine which cylinder will have a greater moment of inertia about the central axis.
2. Moment of Inertia:
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. For a cylinder, the moment of inertia depends on its mass, radius, and shape.
3. Moment of Inertia of a Hollow Cylinder:
The moment of inertia of a hollow cylinder is given by the formula:
I = MR²
where M is the mass of the cylinder and R is its radius. In this case, both cylinders have the same mass and radius. Therefore, the moment of inertia of the hollow cylinder is proportional to the square of its radius.
4. Moment of Inertia of a Solid Cylinder:
The moment of inertia of a solid cylinder is given by the formula:
I = (1/2)MR²
where M is the mass of the cylinder and R is its radius. Again, both cylinders have the same mass and radius. Therefore, the moment of inertia of the solid cylinder is also proportional to the square of its radius, but with a factor of (1/2) compared to the hollow cylinder.
5. Comparison:
Since the moment of inertia of the hollow cylinder is proportional to the square of its radius, and the moment of inertia of the solid cylinder is also proportional to the square of its radius but with a factor of (1/2), we can conclude that the moment of inertia of the hollow cylinder will be greater than that of the solid cylinder.
6. Conclusion:
Therefore, the correct answer is option 'A' - the hollow cylinder will have a greater moment of inertia about the central axis compared to the solid cylinder.
1. Introduction:
In this question, we are given two cylinders with the same mass and radius. One cylinder is hollow, while the other is solid. We need to determine which cylinder will have a greater moment of inertia about the central axis.
2. Moment of Inertia:
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. For a cylinder, the moment of inertia depends on its mass, radius, and shape.
3. Moment of Inertia of a Hollow Cylinder:
The moment of inertia of a hollow cylinder is given by the formula:
I = MR²
where M is the mass of the cylinder and R is its radius. In this case, both cylinders have the same mass and radius. Therefore, the moment of inertia of the hollow cylinder is proportional to the square of its radius.
4. Moment of Inertia of a Solid Cylinder:
The moment of inertia of a solid cylinder is given by the formula:
I = (1/2)MR²
where M is the mass of the cylinder and R is its radius. Again, both cylinders have the same mass and radius. Therefore, the moment of inertia of the solid cylinder is also proportional to the square of its radius, but with a factor of (1/2) compared to the hollow cylinder.
5. Comparison:
Since the moment of inertia of the hollow cylinder is proportional to the square of its radius, and the moment of inertia of the solid cylinder is also proportional to the square of its radius but with a factor of (1/2), we can conclude that the moment of inertia of the hollow cylinder will be greater than that of the solid cylinder.
6. Conclusion:
Therefore, the correct answer is option 'A' - the hollow cylinder will have a greater moment of inertia about the central axis compared to the solid cylinder.
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Community Answer
Two cylinders have the same mass and radius. One is hollow and the oth...
The hollow one will have greater density as both have the same mass and it has to be distributed uniformly. Thus, the summation of product of mass and perpendicular distance from the axis squared of each particle will be more for the hollow cylinder. And hence, it has more moment of inertia.
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Two cylinders have the same mass and radius. One is hollow and the other is solid. Which one will have the greater moment of inertia about the central axis?a)Hollow cylinderb)Solid cylinderc)Same for bothd)Depends on length of cylinderCorrect answer is option 'A'. Can you explain this answer?
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Solutions for Two cylinders have the same mass and radius. One is hollow and the other is solid. Which one will have the greater moment of inertia about the central axis?a)Hollow cylinderb)Solid cylinderc)Same for bothd)Depends on length of cylinderCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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