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  4. Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is Io as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

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Q. Moment of inertia of an equilateral triangular lamina $ABC$, about the axis passing through its centre $O$ and perpendicular to its plane is $I_o$ as shown in the figure. A cavity $DEF$ is cut out from the lamina, where $D, E, F$ are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :Physics Question Image

JEE MainJEE Main 2017System of Particles and Rotational Motion

Solution:

$I_{0} = kml^{2}\quad\quad\quad BC = l$
$I_{DEF} = k \frac{m}{4} \left(\frac{l}{2}\right)^{2}$
$= \frac{k}{16}\,ml^{2}$
$I_{DEF} = \frac{I_{0}}{16}$
$I_{remain} = I_{0} = \frac{I_{0}}{16}$
$= \frac{15I_{0}}{16}$