Question

Three uniform circular discs, each of mass $M$ and radius $R$ are kept in contact with each other as shown in figure. Moment of inertia of the system about the axis AB is:

• A. $\frac{11}{4}M{R}^2$
• B. $\frac{11}{2}M{R}^2$
• C. $\frac{M{R}^2}{2}$
• D. $\frac{M{R}^2}{4}$

Answer 1

Answer: (A)

$\frac{11}{4}M{R}^2$

Moment of inertia of disc about an axis passing through its center of mass and parallel to its plane

$I=\frac{1}{4}M{R}^2$

$\therefore$ MI of disc $S$ about line $AB$, $I_S=\frac{1}{4}M{R}^2$ .........(1)

Let MI of discs $P$ and $Q$ about line $AB$ be $I_P$ and $I_Q$ respectively.

For disc $P$ :

Using parallel axis theorem, $I_p=\frac{1}{4}M{R}^2+M{R}^2=\frac{5}{4}M{R}^2$ ...........(2)

Similarly, $I_Q=\frac{5}{4}M{R}^2$ ......(3)

$\therefore$ Moment of inertia of the system about $AB$ $I_{AB}=I_S+I_P+I_Q$

$\therefore$ $I_{AB}=\frac{1}{4}M{R}^2+\frac{5}{4}M{R}^2+\frac{5}{4}M{R}^2=\frac{11}{4}M{R}^2$