Question

Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is 'I₁'. The same rod is bent into a ring and its moment of inertia about the diameter is 'I₂', then `"I"_2/"I"_1` is ______.

Options

• `3/(2pi^2)`

• `3/(4pi^2)`

• `(2pi^2)/3`

• `(4pi^2)/3`

Answer 1

Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is 'I₁'. The same rod is bent into a ring and its moment of inertia about the diameter is 'I₂', then `"I"_2/"I"_1` is `underline(3/(2pi^2))`.

Explanation:

`"I"_1="ML"^2/12`

when the rod is bent into a ring,

L = 2πr or `r="L"/(2pi)`

Moment of inertia of a ring about a diameter is given by

`"I"_2="Mr"^2/2="M"/2*"L"^2/(4pi^2)="ML"^2/(8pi^2)`

`therefore"I"_2/"I"_1="ML"^2/(8pi^2)xx12/"ML"^2=3/(2pi^2)`