Question

Three identical rings of mass Meach and radius R
are joined as shown in figure. If moment of inertia
about an axis passing through point o and
perpendicular to the plane of rings is equal to (O is
geometrical centre of system) kMR², then value of k is​

Answer 1

Answer:

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Answer 2

Given:

• three identical rings of mass M and radius R

• the moment of inertia about an axis passing through point o and perpendicular to the plane of ring is equal to $kMR^{2}$ ( O is geometrical centre of system)

To find: The value of k ?

Explanation:

the moment of inertia of a ring about the axis passing through its centre and perpendicular to the plane of ring is given by,

                                                $I = MR^{2}$

Now we know that,

the moment of inertia of the whole system will be the moment of inertia of one ring about the axis passing through its centre and for the other rings the axis will be 2R distance from the centre.

Now using the parallel axis theorem we can find out the moment of inertia of the other ring which will be,

                                      $I_{2} = MR^{2} + M(2R)^{2} = 5MR^{2}$

so total moment of inertia will be,

                                      $I = I_{1} +2I_{2} = MR^{2} +2$ × $5MR^{2}$

                                              = $11MR^{2}$

                                            k = 11

Hence the value of k is 11.