A block of mass $15 \,kg $ is resting on a rough inclined plane as shown in figure. The block is tied up by a horizontal string which has tension of $50\,N$. The minimum coefficient of friction between the surfaces of contact is $(g = 10\,m/s^2)$
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The string is under tension, hence there is liming friction between the block and the plane. Drawing free body diagram of the block
$\Sigma F x=0$
$\Rightarrow \quad \mu N+50 \cos 45^{\circ}=150 \sin 45^{\circ}$ $...(i)$
$\Sigma F_{y}=0$
$\Rightarrow \quad \mathrm{N}=50 \sin 45^{\circ}+150 \cos 45^{\circ} \ldots(ii)$
Solving $(i)$ and $(iii)$ we get
$\mu=\frac{1}{2}$
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