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Question

If the coefficient of friction between A and B is μ, the minimum horizontal acceleration of the wedge A for which B will remain at rest w.r.t. the wedge is

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

The correct option is D g(1μ1+μ)
Solving in wedge's frame,
To keep block B at rest, from FBD of block B we get

masin45+fs=mgsin45 ... (1)
R=mgcos45+macos45 ... (2)
From (1) & (2) and using fs=μsR
masin45+μ(mgcos45+macos45)=mgsin45
ma+μ(mg+ma)=mg
a(1+μ)=g(1μ)
a=g(1μ1+μ)

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