At the bottom edge of a smooth vertical wall, an inclined plane is kept at an angle of 45° from the horizontal.A uniform ladder of length ℓ and mass M rests on the inclined plane against the wall such

Question

At the bottom edge of a smooth vertical wall, an inclined plane is kept at an angle of 45° from the horizontal.A uniform ladder of length $ℓ$ and mass M rests on the inclined plane against the wall such that it is perpendicular to the inclined, as shown in the figure. The minimum coefficient of friction necessary so that the ladder does not slip on the incline is found to be $1/ α$ . Find the value of $α$ .

CT44 full source figure

TestHub · Accepted Answer

Torque balance gives friction f=Mg/(2√2). Force balance gives normal N=3Mg/(2√2). Thus μ=f/N=1/3, so α=3.

Physics - Rotation Question with Solution | TestHub

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