Question

Three identical rings of mass m and radius r are

placed as shown in figure. Find moment of inertia

of the system about axis ' XX ?​

Answer 1

Answer:

moment of inertia of shell w.r.t. axis passing through it's center

I

C.M.

=

3

2

MR

2

moment of inertia of shell w.r.t. axis tangent to shell can be found using parallel axis theorem

I

tangent

=I

C.M.

+MR

2

=

3

2

MR

2

+MR

2

=

3

5

MR

2

total m.o.i. with respect to given axis

=I

xx

=I

1

+I

2

+I

3

=

3

2

MR

2

+2×

3

5

MR

2

=

3

12

MR

2

=4mR

2

hence, correct answer is option B = 4mr^2