Question

5-11 Two identical semicircular discs of mass ' $m$ ' each and radius ' $R$ ' are placed in the $X Y$ (horizontal) plane and the $Y Z$ (vertical) plane, respectively. They are so placed that they have their common diameter along the $Y$-axis. Then, the moment of inertia $\left(I_{n}\right)$ of the system about the appropriate axis is given by $\left(I_{n}\right.$ refers to moment of inertia about axis $n$-where $n$ is $X, Y, Z$ )

• A. $l_{X}=\frac{1}{2} m R^{2}$
• B. $l_{Y}=\frac{1}{2} m R^{2}$
• C. $l_{Z}=\frac{3}{4} m R^{2}$
• D. $l_{X}=l_{Y}=l_{Z}$

Answer 1

Answer: (B), (C)

From figure we have
$I_{Y}=\frac{1}{2} m R^{2} \quad \& I_{X}=I_{Z}=\frac{3}{4} m R^{2}$