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  4. A circular disc D1 of mass M and radius R has two identical discs D2 and D3 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 D1, as shown in the figure, will be :

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Q. 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 :Physics Question Image

JEE MainJEE Main 2019System of Particles and Rotational Motion

Solution:

$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} $