Question

A circular disc $D_1$ of mass $M$ and radius $R$ has two identical discs $D_2$ and $D_3$ of the same mass $M$ and radius $R$ attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis $OO'$, passing through the centre of $D_1$, as shown in the figure, will be :

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

Answer 1

Answer: (A)

$3 MR^2$

Answer 2

$I = \frac{MR^{2}}{2} + 2\left(\frac{MR^{2}}{4} + MR^{2}\right)$
$= \frac{MR^{2}}{2} + \frac{MR^{2}}{2} + 2 MR^{2}$
$= 3\, MR^{2}$