A square plate of mass ‘M’ and edge ‘L’ it shown. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle $15^{o}$ from horizontal is $\frac{11 {ML}^{2}}{8 x}$ Where ‘x’ is

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Detailed Solution

$I_{x} + I_{y} = I_{z}$

By similarity we can say I_x and I_y are equal

$\Rightarrow I_{x} = I_{y} = \frac{I_{z}}{2}$

$So, I_{x} = I_{y} = \frac{{ML}^{2}}{12}$

from the above figure

$I^{'} = I_{x} + {Mr}^{2} = \frac{{ML}^{2}}{12} + M {(\frac{\sqrt{3} L}{2 \sqrt{2}})}^{2} = \frac{{ML}^{2}}{12} + \frac{3 L^{2}}{8}$

$\Rightarrow I^{'} = \frac{11 M}{24} L^{2}$

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