Two uniform boards, tied together with the help of a string, are balanced on a surface as shown in Fig.
The coefficient of static friction between boards and surface is `0.5`. The minimum value of `theta`, for which this type of arrangement is possible is

Options

A. `30^@`
B. `45^@`
C. `37^@`
D. it is not possible to have this type of balanced arrangement

Answer

B

Explanation

For the equilibrium of the entire structure `N_(1)+N_(2)=2Mg`

`Mg(l/2costheta)+N_(2)xx2x-Mg(l/2costheta+2x)=0`
Given `N_(2)=Mg, N_(1)=Mg`
For individual boards, `T_(1)=f_(1), N_(2)=Mg`
and `T_(1)xxlsintheta=(Mg)/(2tantheta)`
For safe equilibrium `f_(1)ltf_(L)=mu_(s)Mg`
`(Mg)/(2tantheta)=mu_(s) Mgimpliestanthetagt1/(2mu_(s))impliestheta=45^@`
So the minimum value of `theta` for this type of arrangement is `45^@`