Question

Three discs having same mass $M$ and radius $R$ are placed as shown in figure. Then the moment of inertia of system about axis $AB$ in the given arrangement is –

• A. $2M{R}^2$
• B. $3M{R}^2$
• C. $\frac{5M{R}^2}{4}$
• D. $6M{R}^2$

Answer 1

The correct option is B $3M{R}^2$

Moment of Inertia of the system can be formulated as
$I=I_1+I_2+I_3$
$I_1=\frac{M{R}^2}{2}=$Moment of Inertia about centre of disc
$I_2=I_3=\frac{M{R}^2}{4}+M{R}^2=$ Moment of Inertia of other two discs about AB (parellel axis theorem)
$\Rightarrow \frac{M{R}^2}{2}+2(\frac{M{R}^2}{4}+M{R}^2)$
$\Rightarrow 3M{R}^2$