Moment of inertia of an equilateral triangular lamina ABC, about the… | JEE Main 2017 (8 Apr, Shift 1)

Q173JEE Main 2017 · 8 APR · SHIFT 1Difficult

Moment of Inertia & Radius of Gyration

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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Answer: (b)

DEF is equilateral with side $\frac{a}{2}$ and the same centre O; its mass is $\frac{M}{4}$ .
$I \propto Ma^2$ , so $I_{DEF} = \frac{1}{4} \times \frac{1}{4}I_0 = \frac{I_0}{16}$
$I = I_0 - \frac{I_0}{16} = \frac{15}{16}I_0$ , so the answer is (b).

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