Question

A symmetrical lamina of mass $M$ consists of a square shape with a semicircular section over each of the edge of the square as shown. The moment of inertia of the lamina about an axis through the centre of mass and perpendicular to the plane is $1.6Ma^{2}.$ The moment of inertia about the tangent $AB$ in the plane of the lamina is:

• A. $4.8Ma^{2}$
• B. $2.6Ma^{2}$
• C. $1.8Ma^{2}$
• D. $7.2Ma^{2}$

Answer 1

Answer: (A)

Moment of inertia about the line $AB$ is given by,
$I_{A B}=I_{x}+M\left(2 a\right.$, where $I_{ X }=$ moment of inertia of lamina with respect to $X -$ axis.
Therefore,
$I_{AB}=\left(\frac{1 . 6 M a^{2}}{2}\right)+4Ma^{2}$
$\Rightarrow I_{AB}=4.8Ma^{2}$