First slide

Moment of intertia

Question

Two thin rings, each of mass m and radius R are rigidly attached with each other as shown in figure. Then moment of inertia of the system of rings about the diameter AB is

Moderate

A

$\frac{3}{4} m R^{2}$
B

$2 m R^{2}$
C

$\frac{5}{2} m R^{2}$
D

$\frac{3}{2} m R^{2}$

Solution

For ring (1), ${(I_{A B})}_{1} = \frac{1}{2} m R^{2}$
For ring (2), ${(I_{A B})}_{2} = m R^{2} + m R^{2} = 2 m R^{2}$
$∴ {(I_{A B})}_{system} = \frac{1}{2} m R^{2} + 2 m R^{2} = \frac{5}{2} m R^{2}$

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