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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 will remain at rest with respect to wedge is

  1. g[1+μ1μ]
  2. μg
  3. g[1μ1+μ]
  4. gμ


Solution

The correct option is A g[1+μ1μ]
By placing the frame of reference on block A, FBD of B is

Let, N be the normal force acting. Now taking components of all the forces perpendicular to the plane
Nmgcosθmasinθ=0
N=mg+ma2
As, f=μN
f=μm(g+a)2
Taking mg and ma along f 
mgsinθ+f=macosθ
mg2+μm(g+a)2=ma2
a=g[1+μ1μ]

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