Question

6. Moment of inertia of a thin uniform rod rotating
about the perpendicular axis passing through its
centre is I. If the same rod is bent into a ring and its
moment of inertia about its diameter is I', then the
ratio I/I' is​

Answer 1

Explanation:

We have:

Moment of inertia of rod rotating about an axis passing through one end: I=\dfrac { m{ l }^{ 2 } }{ 3 } I=

3

ml

2

Moment of inertia of ring rotating about one of its diameters: { I }_{ 1 }=\dfrac { m{ r }^{ 2 } }{ 2 } I

1

=

2

mr

2

Since the rod is bent into a ring, the circumference of the ring and the length of the rod are equal: