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 edges. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes and angle $\theta$ with AB The moment of inertia of the plate about the axis $CD$ is then equal to

• A. $I$
• B. $I{\sin }^2\theta$
• C. $I{\cos }^2\theta$
• D. $I{\cos }^2\left(\theta /2\right)$

Answer 1

Answer: (A)

$I$

$\text{Given - A square plate and moment of Inertia I}$

$\text{about the}a\times i\text{s}AB$

$\begin{array}{c}\text{In case of a}2-D\text{symmetrical body. The}\\ \text{moment of Inertia of a body about all the}\\ \text{axes passing through its centre of symmety}y\\ \text{and lying in the plane of body is same}\\ \text{Hence}\to I_{cD}=I_{AB}=I\\ \text{Henu, correct opion is}\left(A\right)\end{array}$