Question

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 :

• A. $\frac{7}{8} I_o$
• B. $\frac{15}{16} I_o$
• C. $\frac{3I_o}{4}$
• D. $\frac{3 1I_o}{32}$

Answer 1

Answer: (B)

$\frac{15}{16} I_o$

Answer 2

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