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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 :

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 45oFor the equilibrium of the entire structure, N1+N2=2MgMg(12cosθ)+N2×2x−Mg(12cosθ+2x)=0Given N2=Mg,N1=MgFor individual boards, T1=f1,N1=Mgand T1×lsinθ=Mg12cosθf1=T1=Mg2tanθFor safe equilibrium, f1<fL=μsMgMg2tanθ=μsMg⇒tanθ>12μs⇒θ=45oSo the minimum value of θ for this type of arrangement is 45o

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