Linear mass density of the two rods system, AC and CD is x. moment of inertia of two rods about an axis passing through AB is

Options

A. `(xl^(3))/(4sqrt(3))`
B. `(xl^(3))/(sqrt(2))`
C. `(xl^(3))/(4)`
D. `(xl^(3))/(6sqrt(2))`

Answer

D

Explanation

`L=(l)/(2)sec45^(@)=(1)/(sqrt(2))`
`m=Lx=(lx)/(sqrt(2))`
`I=2[(mL^(2))/(3)sin^(2)45^(@)]`
`=[((lx)/(3sqrt(2)))((l)/(sqrt(2)))^(2)((1)/(2))]`
`=(xl^(3))/(6sqrt(2))`