A symmetric lamina of mass M consists of a square shape with a semicircular section over of the edge of the square as shown in fig. p-10. The side of the square is 2a. The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is `1.6Ma^2`. The moment of inertia of the lamina is ......

Options

A. `2.4Ma^(2)`
B. `3.6Ma^(2)`
C. `4.8Ma^(2)`
D. `6.00Ma^(2)`

Answer

C

Explanation

If the lamina lies in the X-Y plane, then from the perpendicular axis theorem
`I_(z)=I_(x)+I_(y)" but by symmetry, "I_(x)=I_(y)`
`therefore I_(z)=2I_(x)`
`therefore I_(x)=(I_(z))/(2)=(1.6Ma^(2))/(2)=0.8Ma^(2)`
and from the parallel axes theorem
`I_(AB)=I_(x)+M(2a)^(2)=0.8Ma^(2)+4Ma^(2)=4.8Ma^(2)`