Question

A thin uniform rod has a moment of inertia of 1 kgmsquare about a perpendicular axis through its centre. If it is bent to form a circular ring,what is the moment of inertia about its diameter.?

Answer 1

Explanation:

Let the length of the rod be L and mass be M.

Then, moment of inertia of the rod about a perpendicular axis through the center is given by:

I=

12

ML

2

......(i)

Now, the rod is bent in the shape of a ring. Hence, the circumference of the ring equals the length of the rod.

∴L=2πR...............(ii) where R is the radius of the ring

Moment of inertia of ring about its diameter is given by:

I

′

=

2

MR

2

.....................(iii)

From (i), (ii) and (iii),

I

′

I

=

2

MR

2

12

ML

2

=

6R

2

L

2

=

6R

2

(2πR)

2

=

3

2π

2

Please mark me as Brainalist if it helps and follow me