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  • With reference to Fig. 7.6 of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)

With reference to Fig. 7.6 of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)

(a) The moment of inertia of cube about z-axis is I_{z}=I_{x}+I_{y}

(b) The moment of inertia of cube about z' is I'_{z}=I_{z}+\frac{m\; a^{2}}{2}

(c) The moment of inertia of cube about z'' is =I_{z}+\frac{m\; a^{2}}{2}

(d) I_{x}=I_{y}

Answers (1)

The correct answer is the option (a), (b), and (d).

 By perpendicular axis theorem I_{z}=I_{x}+I_{y}

So a is correct

Z and z' axis are parallel, and the distance between them can be calculated as \frac{DG}{2}

\frac{DG}{2}=\frac{1}{2}\sqrt{a^{2}+a^{2}}=\frac{a}{\sqrt{2}}

By parallel axis theorem I'_{z}=I_{z}+M(\frac{a}{\sqrt{2}})^{2}=I_{z}+\frac{Ma^{2}}{2}

So b is correct

Since Z-axis and z" axis are not parallel to each other, so parallel theorem is not applicable here, rendering option c wrong

Since Z axis passes through the centre of the cube, so x and y-axis are symmetric I_{x}=I_{y}

Hence, d is correct

Posted by

infoexpert23

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