If the coefficient of friction between `A` and `B` is `mu`, the maximum acceleration of the wedge `A` for which `B` will remain at rest with respect to the wedge is

Options

A. `mu g`
B. `g((1+mu)/(1 - mu))`
C. `(g)/(mu)`
D. `g((1-mu)/(1 + mu))`

Answer

B

Explanation

FBD of block B w.r.t. wedge A , for maximum 'a' ,

Perpendicular to wedge :
`Sigma f_(y) =(mg cos theta + mas sin theta-N)=0`
and `Sigma f_(x) =mg sin theta + muN - ma cos theta = 0` (for maximum a)
`rArr mg sin theta + mu(mg cos theta + ma sin theta)`
`-ma cos theta = 0`
`rArr a =((g sin theta + mu g cos theta))/(cos theta - mu sin theta)`
for `theta = 45^(@)`
`a=g((tan 45^(@) +mu)/(cot 45^(@) -mu)), a =g ((1+mu)/(1-mu))`.