First slide

Moment of intertia

Question

Three rings each of mass M and radius R are arranged as shown in fig. (s). The moment of inertia of the
system about YY' will be

Moderate

A

$\frac{3}{2} {MR}^{2}$
B

3M R²
C

$\frac{7}{2} {MR}^{2}$
D

5 M R²

Solution

The moment of inertia about Y Y'-axis is given by
$\begin{array}{l} I = I_{A} + I_{B} + I_{C} \\ = I_{A} + 2 I_{B} (∵ I_{B} = I_{C}) \\ = \frac{{MR}^{2}}{2} + 2 [\frac{{MR}^{2}}{2} + {MR}^{2}] \\ ∵ ∵ I_{B} = (\frac{{MR}^{2}}{2} + {MR}^{2}) \end{array}$
(Applying the theorem of parallel axes)
$= \frac{7}{2} {MR}^{2}$

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