Question

State an expression for the moment of inertia of a thin, uniform rod about an axis passing
through its centre and perpendicular to its length.

Answer 1

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11th

Physics

Systems of Particles and Rotational Motion

Moment of Inertia

Moment of Inertia of a thin...

PHYSICS

Asked on October 15, 2019 byPrakrati Bukhari

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

A

3π2/2

B

8π2/3

C

2π2/3

D

5π2/3

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VIDEO EXPLANATION



ANSWER

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=12ML2......(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′=2MR2.....................(iii)

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

I′I=2MR212ML

Explanation:

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