Find out the moment of inertia of the following structure `(` written as `PHYSICS)` about axis `AB` made of thin uniform rods of mass per unit length `lambda`.

Answer

`13 lambda l^(3)`

Explanation

The moment of inertia of all seven rods parallel to `AB` and not lying on `AB` is
`=7xx(lambda l ) l^(2)=7 lambda l^(3)`
the moment of inertia of all five rods lying on `AB=0`
The moment of inertia of all 18 rods perpendicular to `AB` is `=18(lambda l)(l^(2))/(3)=6lambda l^(3)`
Hence net `MI` of rod about `AB`
`=7 lambda l^(3)+6lambdal^(3)=13 lambdal^(3)Ans.`