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# three rings each of mass m and radius r are so placed that they touch each other

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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 hereπto get an answer to your question βοΈ 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 β β r

B

6 5 β β r

C

7 6 β β r

D

6 7 β β 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 β = 2 1 β 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 β = 2 1 β mr 2 + mr 2 = 2 3 β 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 β = 2 3 β mr 2

Step 3:: fining total momentum

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

1 β +I 2 β +I 3 β = 2 7 β mr 2 3 m I β β = 6 7 β β 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

Text Solution Open Answer in App A 6 5 β β β r 65r B 5 6 β β β r 56r C 6 7 β β β r 67r D 7 6 β β β r 76r 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

Home

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 β 7 6 r B β 5 3 r C β 5 6 r D β 7 2 r Open in App Solution

The correct option is A

β 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 , β΄ I = I 1 + I 2 + I 3 = 7 2 m r 2

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

β΄ 3 m k 2 = 7 2 m r 2 β k = β 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

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

, 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

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

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

Guys, does anyone know the answer?