Question

Two thin discs each of mass $M$ and radius $r$ are attached as shown to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc $B$ and passing through its centre is

• A. $2\, M r^{2}$
• B. $3\, M r^{2}$
• C. $4\, M r^{2}$
• D. $5\, M r^{2}$

Answer 1

Answer: (D)

Moment of inertia of each disc about an axis through
the centre and perpendicular to the plane is $I_{A}=I_{B}=\frac{1}{2} M r^{2}$
Applying theorem of parallel axes, moment of inertia of disc $A$
about the given axis is $I_{A}^{\prime}=\frac{1}{2} M r^{2}+M(2 r)^{2}=\frac{9}{2} M r^{2}$
$\therefore I=I_{A}^{\prime}+I_{B}=\frac{9}{2} M r^{2}+\frac{1}{2} M r^{2}=5 M r^{2}$