In a rectangle `ABCD` (`BC=2 AB`). The moment of inertia along which the axis will be minimum

Options

A. `BC`
B. `BD`
C. `HF`
D. `EG`

Explanation

The moment of inertia will be minimum about that axis, which is passing through the center of mass.

`I_(EG)=(MB^(2))/(12)`
`I_(FH)=(M(2B)^(2))/(12)=(MB^(2))/(6)`
`M.I.` of the rectangular plate about its diagonal
`I_(BD)=(MB^(2)L^(2))/(6(B^(2)+L^(2)))=(MB^(2)xx4B^(2))/(6(B^(2)+4B^(2)))=(2)/(15)MB^(2)=(MB^(2))/(7.5)`
`M.I.` about `EG` is minimum.
OR
By observation, distribution of mass is the nearest about axis `EG`.