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Question

If the coefficient of friction between A and B is μ, the maximum acceleration of the wedge A for which B remains at rest with respect to the wedge is



A
μg
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B
g(1+μ1μ)
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C
g(1μ1+μ)
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D
gμ
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Solution

The correct option is B g(1+μ1μ)
The FBD of B is
Here the block B experiences pseudo force towards left in the A frame.
By balancing the equation perpendicular to the incline we get,

N=masinθ+mgcosθ

Now balancing the forces along the incline plane,
macosθ=mgsinθ+f
In limiting case, (f=μN)
Hence we get,
masinθ=mgsinθ+μ(masinθ+mgcosθ)

By putting θ=45o we get,
a×12=g×12+μ(a×12+g×12)

a=g(1+μ1μ)

Hence option B is the correct answer


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