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/(2sqrt(3)))`
C. `tan^(-1)(1/(3sqrt(3)))`
D. `tan^(-1)(1/(4sqrt(3)))`

Answer

C

Explanation

F.B.D of A
`2N cos 30^(@) = mg`
F.B.D of C
Net force along the inclined plane `=0`
`N cos (60^(@)+theta)=mg sin theta`
`"Solving" tantheta=1/(3sqrt(3))`