AP EAPCET 08-Jul-2022 Shift 1 Paper

For a rectangular lamina moment of inertia about its centroidal axis given by

ICM=

Vc

12

(a2+b2)

Now, moment of inertia of lamina about an axis passing through one of vertices is obtained by using parallel axis theorem.



Now, moment of Inertia about any vertex,
Icorner =ICM+m⋅d2
d= distance between axes
Icorner =

m

12

(a2+b2)+md2
Now from diagram,
d2=(

a

2

)2+(

b

2

)2
Icorner =

m

12

(a2+b2)+m(‌

a2+b2

4

)
=m(

a2+al2+b2+3b2

12

)
=m(

4(a2+b2)

12

)
=m(

a2+b2

3

)=

1

3

m(a2+b2)