Question

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$ . The moment of inertia of the plate about the axis $CD$ is then equal to

• A. $I$
• B. $Isi{n}^2\theta$
• C. $Ico{s}^2\theta$
• D. $Ico{s}^2\frac{\theta }{2}$

Answer 1

Answer: (A)

From symmetry $I_{AB}=I_{A^{\prime }{B}^{\prime }}$ and $I_{CD}=I_{C^{\prime }{D}^{\prime }}$

From theorem of perpendicular axes
${\text{I}}_{zz}={\text{I}}_{\text{AB}}+{\text{I}}_{A^{\prime }{B}^{\prime }}={\text{I}}_{\text{CD}}+{\text{I}}_{\text{C’D’}}$
$I_{zz}=2{\text{I}}_{\text{AB}}$
$I_{zz}=2{\text{I}}_{\text{CD}}$
$\therefore I_{CD}=I_{C^{\prime }{D}^{\prime }}$