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:
`Sigmaf_(y')=(mg cos theta+m a sin theta-N)=0`
and `Sigma f_(x')=mg sin theta+mu N -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((tan45^(@)+mu)/(cot 45^(@)-mu)), a=g((1+mu)/(1-mu))`