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Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. the moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 1)181/2 MR^2 2)19/2 MR^2 3) 55/2 MR^2 4) 73/2 MR^2?
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The moment of inertia of the arrangement can be calculated by considering the moment of inertia of each individual disk and the parallel axis theorem.
1. Moment of inertia of an individual disk:
The moment of inertia of a circular disk about an axis perpendicular to its plane and passing through its center is given by the formula:
I = (1/2) * M * R^2
where I is the moment of inertia, M is the mass of the disk, and R is the radius of the disk.
2. Calculation of the moment of inertia of the arrangement:
Since all the disks are identical and symmetrically welded, the moment of inertia of the arrangement can be obtained by considering the moment of inertia of one disk and multiplying it by the total number of disks.
I_arrangement = 7 * I_disk
3. Application of the parallel axis theorem:
The moment of inertia of the arrangement is calculated with respect to an axis passing through point P, which is not the center of mass of the arrangement. We can use the parallel axis theorem to calculate this moment of inertia.
The parallel axis theorem states that the moment of inertia about an axis parallel to an axis passing through the center of mass is equal to the sum of the moment of inertia about the center of mass and the product of the mass and the square of the perpendicular distance between the two axes.
Therefore, the moment of inertia of the arrangement about the axis passing through point P is given by:
I_P = I_arrangement + M * d^2
where I_P is the moment of inertia about point P, I_arrangement is the moment of inertia of the arrangement, M is the mass of each disk, and d is the perpendicular distance between the center of mass of the arrangement and point P.
4. Calculation of the moment of inertia:
Substituting the value of I_arrangement from step 2 into the equation from step 3, we get:
I_P = 7 * I_disk + M * d^2
Since I_disk = (1/2) * M * R^2, we have:
I_P = 7 * (1/2) * M * R^2 + M * d^2
Simplifying the equation, we get:
I_P = (7/2) * M * R^2 + M * d^2
Comparing this equation with the given options, we can see that the correct answer is option 3) 55/2 MR^2.
Therefore, the moment of inertia of the arrangement about the axis normal to the plane and passing through point P is 55/2 MR^2.
1. Moment of inertia of an individual disk:
The moment of inertia of a circular disk about an axis perpendicular to its plane and passing through its center is given by the formula:
I = (1/2) * M * R^2
where I is the moment of inertia, M is the mass of the disk, and R is the radius of the disk.
2. Calculation of the moment of inertia of the arrangement:
Since all the disks are identical and symmetrically welded, the moment of inertia of the arrangement can be obtained by considering the moment of inertia of one disk and multiplying it by the total number of disks.
I_arrangement = 7 * I_disk
3. Application of the parallel axis theorem:
The moment of inertia of the arrangement is calculated with respect to an axis passing through point P, which is not the center of mass of the arrangement. We can use the parallel axis theorem to calculate this moment of inertia.
The parallel axis theorem states that the moment of inertia about an axis parallel to an axis passing through the center of mass is equal to the sum of the moment of inertia about the center of mass and the product of the mass and the square of the perpendicular distance between the two axes.
Therefore, the moment of inertia of the arrangement about the axis passing through point P is given by:
I_P = I_arrangement + M * d^2
where I_P is the moment of inertia about point P, I_arrangement is the moment of inertia of the arrangement, M is the mass of each disk, and d is the perpendicular distance between the center of mass of the arrangement and point P.
4. Calculation of the moment of inertia:
Substituting the value of I_arrangement from step 2 into the equation from step 3, we get:
I_P = 7 * I_disk + M * d^2
Since I_disk = (1/2) * M * R^2, we have:
I_P = 7 * (1/2) * M * R^2 + M * d^2
Simplifying the equation, we get:
I_P = (7/2) * M * R^2 + M * d^2
Comparing this equation with the given options, we can see that the correct answer is option 3) 55/2 MR^2.
Therefore, the moment of inertia of the arrangement about the axis normal to the plane and passing through point P is 55/2 MR^2.
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Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. the moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 1)181/2 MR^2 2)19/2 MR^2 3) 55/2 MR^2 4) 73/2 MR^2?
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Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. the moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 1)181/2 MR^2 2)19/2 MR^2 3) 55/2 MR^2 4) 73/2 MR^2? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. the moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 1)181/2 MR^2 2)19/2 MR^2 3) 55/2 MR^2 4) 73/2 MR^2? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. the moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 1)181/2 MR^2 2)19/2 MR^2 3) 55/2 MR^2 4) 73/2 MR^2?.
Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. the moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 1)181/2 MR^2 2)19/2 MR^2 3) 55/2 MR^2 4) 73/2 MR^2? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. the moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 1)181/2 MR^2 2)19/2 MR^2 3) 55/2 MR^2 4) 73/2 MR^2? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. the moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: 1)181/2 MR^2 2)19/2 MR^2 3) 55/2 MR^2 4) 73/2 MR^2?.
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