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 ?
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Answer:
Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX' which is touching to two shells and passing through diameter of third shell.
Moment of inertia of the system consisting of these three spherical shells about XX' axis is
Explanation:
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
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