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Question

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 θ, for which this type of arrangement is possible is :

120027_a0b64d21103b4479ba016915b23e141b.png

A
30o
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B
45o
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C
37o
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D
It is not possible to have this type of balanced arrangement.
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Solution

The correct option is B 45o
For the equilibrium of the entire structure, N1+N2=2Mg
Mg(12cosθ)+N2×2xMg(12cosθ+2x)=0
Given N2=Mg,N1=Mg

For individual boards, T1=f1,N1=Mg
and T1×lsinθ=Mg12cosθ
f1=T1=Mg2tanθ

For safe equilibrium, f1<fL=μsMg
Mg2tanθ=μsMgtanθ>12μsθ=45o
So the minimum value of θ for this type of arrangement is 45o

132715_120027_ans_a20943d34db04941ac8674071a649cf4.png

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