Q.

Equilibrium of two Planks on a Rough Plane: Figure shows two planks inclined to horizontal rough surface and connected by a string. Find the minimum angle θ (in degrees) for which this system remain in equilibrium if friction coefficient is μ= 0.5.

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answer is 45.

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Detailed Solution

For equilibrium of plank, we useN=mgT=μN=μmg.For rotational equilibrium of plank we use torque on plank about any point must be zero.τA=mg×l/2cos⁡θ−T×lsin⁡θ=0          mgl2cos⁡θ=μmgl sinθ          tanθ=12μ=1⇒θ=45∘
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