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    Three rings each of mass m and radius r are so placed that they touch each other. The radius or gyration of the system about the axis as shown in the figure is:

    Click hereπŸ‘†to get an answer to your question ✍️ Three rings each of mass m and radius r are so placed that they touch each other. The radius or gyration of the system about the axis as shown in the figure is:

    Question

    Three rings each of mass m and radius r are so placed that they touch each other. The radius or gyration of the system about the axis as shown in the figure is:

    A

    5 6 ​ ​ r

    B

    6 5 ​ ​ r

    C

    7 6 ​ ​ r

    D

    6 7 ​ ​ r Hard Open in App

    Updated on : 2022-09-05

    Solution Verified by Toppr

    Correct option is D)

    correct option is (D) HINT: Moment of inertia is defined as the product of mass of section and the square of the distance between the reference axis and the centroid of the section . Spinning figure skaters can reduce their moment of inertia by pulling in their arms, allowing them to spin faster due to conservation of angular momentum

    Step1:  finding momentum of inertia of upper ring about  axis

    Moment of inertia of the upper ring about the axis I

    1 ​ = 2 1 ​ mr 2

    Now, Momentum of inertia of one the lower ring

    Moment of inertia of the one of the lower ring about the axis I

    2 ​ = 2 1 ​ mr 2 + mr 2 = 2 3 ​ mr 2

    Step 2: finding momentum  of inertia of  of second lower ring

    Similarly, moment of inertia of the second lower ring about the axis I

    3 ​ = 2 3 ​ mr 2

    Step 3:: fining total momentum

    Total moment of inertia of the system about the axis I=I

    Radius of gyration k=

    1 ​ +I 2 ​ +I 3 ​ = 2 7 ​ mr 2 3 m I ​ ​ = 6 7 ​ ​ r

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    Three rings each of mass m and radius r are so placed that they touch each other. The radius of gyration of the system about the axis as shown in the figure is

    Three rings each of mass m and radius r are so placed that they touch each other. The radius of gyration of the system about the axis as shown in the figure i

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    Three rings each of mass m and...

    Three rings each of mass m and radius r are so placed that they touch each other. The radius of gyration of the system about the axis as shown in the figure is

    Updated On: 27-06-2022

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    Text Solution Open Answer in App A 6 5 βˆ’ βˆ’ √ r 65r B 5 6 βˆ’ βˆ’ √ r 56r C 6 7 βˆ’ βˆ’ √ r 67r D 7 6 βˆ’ βˆ’ √ r 76r Answer

    The correct Answer is D

    Answer

    Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

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    Three rings each of mass m and radius r are placed in a plane touching each other as shown. The radius of gyration of the system about the axis as shown in the figure is

    Three rings each of mass m and radius r are placed in a plane touching each other as shown. The radius of gyration of the system about the axis as shown in the figure is

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    Three rings each of mass m and radius r are placed in a plane touching each other as shown. The radius of gyration of the system about the axis as shown in the figure is

    Question

    Three rings each of mass m and radius r are placed in a plane touching each other as shown. The radius of gyration of the system about the axis as shown in the figure is

    A √ 7 6 r B √ 5 3 r C √ 5 6 r D √ 7 2 r Open in App Solution

    The correct option is A

    √ 7 6 r

    Moment of inertia of the system about the given axis,

    I = I 1 + I 2 + I 3 I 1 = m r 2 2 , I 2 = I 3 = 3 2 m r 2 , ∴ I = I 1 + I 2 + I 3 = 7 2 m r 2

    Also, moment of inertia, I = 3mk2, where k is radius of gyration.

    ∴ 3 m k 2 = 7 2 m r 2 β‡’ k = √ 7 6 r

    Suggest Corrections 3

    SIMILAR QUESTIONS

    Q. Three rings each of mass, m and radius, r are placed in a plane touching each other as shown. The radius of gyration of the system about the axis as shown in the figure is

    Q. Three rings each of mass

    m and radius r

    are so placed that they touch each other. The radius of gyration of the system about the axis as shown in the figure is:

    Q. Three rings, each of mass

    m and radius r

    , are so placed that they touch each other. Find the moment of inertia about the axis as shown in figure.

    Q. Four solid rigid balls each of mass

    m and radius r

    are fixed on a rigid-ring of radius

    2 r and mass 2 m

    . The system is whirled about

    β€² O β€²

    as shown. The radius of gyration of the system is

    128 m r 2 / 30. how ?

    Q. Three rings each of mass

    M and radius R

    are arranged as shown in the figure. The moment of inertia of the system about

    A B is:

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    Mohammed 8 day ago
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    Guys, does anyone know the answer?

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