# 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:

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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**

Solve any question of Systems of Particles and Rotational Motion with:-

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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 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

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

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

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

β² O β²

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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