Three identical rigid circular cylinder `A` `B` and `C` are arrenged on smooth inclined surfaces as shown in figure. The laest value of theta that prevent the arrangement from collapes is.

Options

A. `tan^(-1)((1)/(2))`
B. `tan^(-1)((1)/(2sqrt3))`
C. `tan^(-1)((1)/(3sqrt3))`
D. `tan^(-1)((1)/(4sqrt3))`

Answer

C

Explanation

`F.B.D` of `A`
`2N cos 30^(0) =mg`
`F.B.D` of `C`
net force along the inclined plane =0
`N cos(60 +theta) =mg sin theta`
solving `tan theta =(1)/(3sqrt3)`
.