Three rings each of mass ' $M$ ' and radius ' $R$ ' are arranged as shown in the figure. The moment of…
Three rings each of mass ' $M$ ' and radius ' $R$ ' are arranged as shown in the figure. The moment of inertia of system about axis YY' will be
$5 \mathrm{MR}^2$
$\frac{7}{2} \mathrm{MR}^2$
$\frac{3}{2} \mathrm{MR}^2$
$3 \mathrm{MR}^2$
Solution
The moment of inertia of the upper ring about its diameter is given by
$\mathrm{I}_1=\frac{\mathrm{MR}^2}{2}$
The moment of inertia of the two lower rings about a tangent in their plane is given by
$\mathrm{I}_2=\mathrm{I}_3=\frac{3}{2} \mathrm{MR}^2$
Total moment of inertia $\mathrm{I}=\mathrm{I}_1+\mathrm{I}_2+\mathrm{I}_3$
$=\frac{\mathrm{MR}^2}{2}+\frac{3}{2} \mathrm{MR}^2+\frac{3}{2} \mathrm{MR}^2=\frac{7}{2} \mathrm{MR}^2$
